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Structure of the solutions to the system ofcompressible fluid

Research Project

Project/Area Number 22540202
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSaga University

Principal Investigator

KOBAYASHI Takayuki  佐賀大学, 大学院・工学系研究科, 教授 (50272133)

Co-Investigator(Kenkyū-buntansha) KAJIKIYA Ryuji  佐賀大学, 大学院・工学系研究科, 教授 (10183261)
Co-Investigator(Renkei-kenkyūsha) KAGEI Yoshiyuki  九州大学, 大学院・数理学研究院, 教授 (80243913)
MISAWA Masashi  熊本大学, 大学院・自然科学研究科, 教授 (40242672)
IKEHATA Ryo  広島大学, 教育学研究科, 教授 (10249758)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords関数方程式 / 圧縮性流体 / Navier-Stokes 方程式 / Stokes 方程式 / 消散型波動方程式 / 非線形波動方程式 / 線形粘性弾性体方程式 / Navier-Stokes方程式 / Stokes方程式 / Navier-Stokes
Research Abstract

We consider the initial boundary value problems for the semilinear damped wave equations and the semilinear heat equations in two dimension exterior domains. We give the L2 boundedness with respect to the space and time valuables of thesolutions. Also,we consider the zero relaxation time approximation to the compressible Navier-Stokes-Poisson system to derive the mono-polar drift-diffusion system of degenerated type in a framework of the theory of weak solution.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (64 results)

All 2013 2012 2011 2010 Other

All Journal Article (24 results) (of which Peer Reviewed: 24 results) Presentation (40 results) (of which Invited: 6 results)

  • [Journal Article] Fluid Mechanical Approximation to the Degenerated Drift-Diffusion System from Compressible Navier-Stokes-Poisson system2013

    • Author(s)
      T. Kobayashi and T. Ogawa
    • Journal Title

      Indiana University Mathematics Journal.

      Volume: -

    • NAID

      130004604066

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] L2 boundedness for the 2D exterior problems for the semilinear heat and dissipative wave equations2013

    • Author(s)
      T. Kobayashi and M. Misawa
    • Journal Title

      Rims Kokyuroku Bessatsu: Harmonic Analysis and Nonlinear Partial Differential Equations. eds. T. Ozawa, M. Sugimoto

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-radial least energy solutions of the generalized H¥'{e}non equation.2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Differential Equations

      Volume: 252, No.2 Pages: 1987-2003

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow2012

    • Author(s)
      Y. Kagei
    • Journal Title

      Arch. Rational Mech. Anal

      Volume: Vol. 205, no. 2 Pages: 585-650

    • NAID

      120005068801

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy decay estimates for wave equations with a fractional damping2012

    • Author(s)
      R. Ikehata, and M.Natsume
    • Journal Title

      Differential and Integral Eqns

      Volume: 25, No.9-10 Pages: 939-956

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-radial least energy solutions of the generalized H\'{e}non equation2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Differential Equations

      Volume: 252(No.2)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-even least energy solutions of the Emden-Fowler equation2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 140(No.2)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mountain pass theorem in ordered Banach spaces and its applications to semilinear elliptic equations2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Differential Equations

      Volume: 19(No.2)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Least energy solutions of the generalized H\'{e}non equation in reflectionally symmetric or point symmetric domains2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Differential Equations

      Volume: 253(No.5)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-even positive solutions of the one dimensional $p$-Laplace Emden-Fowler equation2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      Applied Mathematics Letters

      Volume: 25(No.11)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay Property for the linear wave equations in two dimensional exterior domains.2011

    • Author(s)
      M. Misawa, S. Okamura and T. Kobayashi
    • Journal Title

      Differential and Integral Equations

      Volume: 63, No.1 Pages: 263-294

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sublinear elliptic equations with singular coefficients on the boundar2011

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Math. Soc. Japan

      Volume: 63, No.1 Pages: 263-294

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global existence of solutions to the compressible Navier-Stokes equation around parallel flows2011

    • Author(s)
      Y. Kagei
    • Journal Title

      J. Differential Equations

      Volume: vol. 251 Pages: 3248-3295

    • NAID

      120005068799

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy decay rates of elastic waves in unbounded domain with potential type of damping2011

    • Author(s)
      R.C.Charaon and R. Ikehata
    • Journal Title

      J. Math. Anal. Appl

      Volume: 380, No.5 Pages: 46-56

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay Property for the linear wave equations in two dimensional exterior domains2011

    • Author(s)
      S.Okamura, T.Kobayashi, M.Misawa
    • Journal Title

      Differential and Integral Equations

      Volume: 24.No.9-10 Pages: 941-964

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sublinear elliptic equations with singular coefficients on the boundary2011

    • Author(s)
      R.Kajikiya
    • Journal Title

      J.Math.Soc.Japan

      Volume: 63.No.1 Pages: 263-294

    • NAID

      10027871371

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of sign-changing solutions for one-dimensional p-Laplacian with a strong singular weight : p-superlinear at infinity2011

    • Author(s)
      R.Kajikiya, Yong-Hoon Lee, Inbo Sim
    • Journal Title

      Nonlinear Analysis, T.M.A.

      Volume: 74.No.17 Pages: 5833-5843

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay Property for the linear wave equations in two dimensional exterior domains.2011

    • Author(s)
      S.Okamura, T.Kobayashi, M.Misawa
    • Journal Title

      Differential and Integral Equations

      Volume: (To appear)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Superlinear elliptic equations with singular coefficients on the boundary2010

    • Author(s)
      R. Kajikiya
    • Journal Title

      Nonlinear Analysis, T.M.A

      Volume: 73, No.7 Pages: 2117-2131

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Local energy decay for a class of hyperbolic equations with constant coefficients near infinity2010

    • Author(s)
      S.Aikawa and R. Ikehata
    • Journal Title

      Math. Nachr

      Volume: 283, No.5 Pages: 636-647

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Superlinear elliptic equations with singular coefficients on the boundary.2010

    • Author(s)
      R.Kajikiya
    • Journal Title

      Nonlinear Analysis, T.M.A.

      Volume: 73.No.7 Pages: 2117-2131

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a criterion for discrete or continuous spectrum of p-Laplace eigenvalue problems with singular sign-changing weights.2010

    • Author(s)
      R.Kajikiya
    • Journal Title

      Nonlinear Analysis, T.M.A.

      Volume: 72.No.7-8 Pages: 3515-3534

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fluid Mechanical Approximation to the Degenerated Drift-Diffusion System from Compressible Navier-Stokes-Poisson system

    • Author(s)
      T. Kobayashi and T. Ogawa
    • Journal Title

      Indiana University Mathematics Journal

    • NAID

      130004604066

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] L2 boundedness for the 2D exterior problems for the semilinear heat and dissipative wave equations

    • Author(s)
      T. Kobayashi and M. Misawa
    • Journal Title

      Rims Kokyuroku Bessatsu: Harmonic Analysis and Nonlinear Partial Differential Equations. eds. T. Ozawa, M. Sugimoto

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Asymptotic behavior of solutions of the compressible Navier-Stokes equation around parallel flows2012

    • Author(s)
      Y. Kagei
    • Organizer
      2012 Fall Trimester Applied Math Colloquium
    • Place of Presentation
      School of Technology Management Ulsan National Institute of Science and Technology (UNIST), Ulsan, Republic of Korea
    • Year and Date
      2012-11-15
    • Related Report
      2012 Final Research Report
  • [Presentation] A regularity for nonlinear parabolic systems of p-Laplacian type with critical growth2012

    • Author(s)
      M. Misawa
    • Organizer
      アールト大学数学解析セミナー
    • Place of Presentation
      アールト大学, Helsinki, Finland
    • Year and Date
      2012-09-11
    • Related Report
      2012 Final Research Report
  • [Presentation] L2 boundedness for the solutions to the 2D Navies-Stokes equations2012

    • Author(s)
      T. Kobayashi
    • Organizer
      Parabolic and Navier-Stokes Equations
    • Place of Presentation
      Banach center, Bedlewo, Poland
    • Year and Date
      2012-09-06
    • Related Report
      2012 Final Research Report
  • [Presentation] L2 boundedness of solutions for the 2D semilinear dissipative wave equations2012

    • Author(s)
      T. Kobayashi
    • Organizer
      RIMS 研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-07-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Energy decay estimates for wave equations with a fractional dampin2012

    • Author(s)
      R. Ikehata
    • Organizer
      第9回 AIMS International Conference on dynamical Systems, Differential equations and Applications
    • Place of Presentation
      Hyatt Regency Grand Cypress, Orlando, Florida, USA
    • Year and Date
      2012-07-04
    • Related Report
      2012 Final Research Report
  • [Presentation] L2 boundedness for the solutions to the 2D Wave equations with damping or strong damping terms2012

    • Author(s)
      小林孝行
    • Organizer
      松山解析セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2012-02-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] Non-radial positive solutions of the H¥'{e}non equation2012

    • Author(s)
      R. Kajikiya
    • Organizer
      International Symposium on Nonlinear Analysis and Optimization 2012
    • Place of Presentation
      Pukyong National University, Pusan, Korea
    • Related Report
      2012 Final Research Report
  • [Presentation] L2 boundedness for the solutions to the 2D semilinear heat equations and the 2D Navier-Stokes equations2012

    • Author(s)
      T. Kobayashi
    • Organizer
      JSPS-DFG Japanese-German Graduate Externship "The 7th Japanese-German International Workshop on Mathematical Fluid Dynamics"
    • Place of Presentation
      Waseda University Tokyo, Japan.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Navier Stokes方程式の解の重み付き減衰評価について2011

    • Author(s)
      小林孝行
    • Organizer
      浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学
    • Year and Date
      2011-12-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Weighted Lp estimates of the solutions to the Navier-Stokes equations in some unbounded domains2011

    • Author(s)
      小林孝行
    • Organizer
      京都大学「NLPDEセミナー」
    • Place of Presentation
      京都大学
    • Year and Date
      2011-12-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] 2次元熱方程式のL2有界性と応用について2011

    • Author(s)
      小林孝行
    • Organizer
      北九州地区における偏微分方程式研究集会
    • Place of Presentation
      九州工業大学
    • Year and Date
      2011-11-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Stokes半群の重み付き評価とNavier-Stokes方程式への応用2011

    • Author(s)
      小林孝行
    • Organizer
      東北大学「応用数学セミナー」
    • Place of Presentation
      東北大学
    • Year and Date
      2011-11-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] 空間遠方で臨界減衰する摩擦項を持つ波動方程式のエネルギー減衰についての新展開2011

    • Author(s)
      R. Ikehata
    • Organizer
      日本数学会秋季総合分科会函数方程式論分科会(特別講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2012 Final Research Report
  • [Presentation] Decay property of solutions to the 2D Wave equations with damping terms or strong damping terms2011

    • Author(s)
      T. Kobayashi
    • Organizer
      Pohang-Kyushu workshop on Partial Differential Equations.
    • Place of Presentation
      POSTECH, Pohang, 韓国
    • Year and Date
      2011-06-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Decay property of solutions to the 2D Wave equations with damping terms or strong damping terms2011

    • Author(s)
      T.Kobayashi
    • Organizer
      Pohang-Kyushu workshop on Partial Differential Equations
    • Place of Presentation
      POSTECH, Pohang,韓国
    • Year and Date
      2011-06-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] Weighted estimates of the solutions to the Navier-Stokes equations in half space and perturbed half-space2011

    • Author(s)
      T. Kobayashi
    • Organizer
      Workshop on Applied Mathematics Euskadi-Kyushu 2011
    • Place of Presentation
      Basque Center for Applied Mathematics, Spain
    • Year and Date
      2011-03-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Weighted estimates of the solutions to the Navier-Stokes equations in half space and perturbed half-space.2011

    • Author(s)
      T.Kobayashi
    • Organizer
      Workshop on Applied Mathematics Euskadi-Kyushu2011
    • Place of Presentation
      Basque Center for Applied Mathematics, Spain.
    • Year and Date
      2011-03-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted L^p estimates of the solutions to the Navier-Stokes equations2011

    • Author(s)
      小林孝行
    • Organizer
      熊本大学応用解析セミナー
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-02-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted estimates of the solutions to the Navier-Stokes equations in half space and perturbed half-space2011

    • Author(s)
      T.Kobayashi
    • Organizer
      第3回名古屋微分方程式研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-02-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted Lp theory for the Stokes resolvent in some unbounded domains2011

    • Author(s)
      T. Kobayashi
    • Organizer
      第4回 日独流体数学国際研究集会
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence of non-radial solutions for the generalized H¥'{e}non equation2011

    • Author(s)
      R. Kajikiya
    • Organizer
      2011 International Workshop on Nonlinear PDE and Applications
    • Place of Presentation
      Pusan National University, Pusan, Korea
    • Related Report
      2012 Final Research Report
  • [Presentation] On the stability of parallel flows of the compressible Navier-Stokes equation2011

    • Author(s)
      Y. Kagei
    • Organizer
      The 3rd Kyushu University-POSTECH Joint Workshop - Partial Differential Equations and Fluid Dynamics
    • Place of Presentation
      POSTECH, Pohang, Korea
    • Related Report
      2012 Final Research Report
  • [Presentation] Weighted Lp theory for the Stokes resolvent in some unbounded domains2011

    • Author(s)
      T.Kobayashi
    • Organizer
      第4回日独流体数学国際研究集会
    • Place of Presentation
      早稲田大学
    • Related Report
      2011 Annual Research Report
  • [Presentation] Weighted Lp-Lq estimates for the Stokes semigroup in some unbounded domains2010

    • Author(s)
      T.Kobayashi
    • Organizer
      Weighted Lp-Lq estimates for the Stokes semigroup in some unbounded domains
    • Place of Presentation
      芝蘭会館別館, 京都
    • Year and Date
      2010-11-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Weighted Lp-Lq estimates for the Stokes semigroup in some unbounded domains2010

    • Author(s)
      T.Kobayasbi
    • Organizer
      研究集会「Partial differential equations and Mathematical Physics」
    • Place of Presentation
      芝蘭会館別館,京都
    • Year and Date
      2010-11-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stokes半群の重み付き評価について2010

    • Author(s)
      小林孝行
    • Organizer
      北九州地区における偏微分方程式研究集会
    • Place of Presentation
      九州工業大学
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted estimates of the solutions to the Navier-Stokes equations in unbounded domains2010

    • Author(s)
      T.Kobayashi
    • Organizer
      日韓共同セミナーによる研究集会:「非線形偏微分方程式に対する正則性特異性に関する研究集会」
    • Place of Presentation
      成均館大学,韓国
    • Year and Date
      2010-10-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted estimates for the Stokes semigroup in half space and perturbed half-space2010

    • Author(s)
      T. Kobayashi
    • Organizer
      Regularity aspects of PDE - a week for Wojciech Zajaczkowski
    • Place of Presentation
      Banach center,Bedlewo,Poland
    • Year and Date
      2010-09-11
    • Related Report
      2012 Final Research Report
  • [Presentation] Weighted estimates for the Stokes semigroup in half space and perturbed half-space2010

    • Author(s)
      T.Kobayashi
    • Organizer
      Regularity aspects of PDE-a week for Wojciech Zajaczkowski
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2010-09-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted estimates for the Stokes semigroup in some unbounded domains2010

    • Author(s)
      小林孝行
    • Organizer
      佐賀大学における微分方程式セミナー
    • Place of Presentation
      佐賀大学
    • Year and Date
      2010-08-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 時間発展 p 調和方程式系に対するヘルダー評価について2010

    • Author(s)
      M. Misawa
    • Organizer
      奈良女子大学偏微分方程式研究集会
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2010-06-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Conference on dynamical Systems2010

    • Author(s)
      R. Ikehata
    • Organizer
      Differential equations and Applications
    • Place of Presentation
      Dresden University of Technology, Dresden, Germany
    • Year and Date
      2010-05-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Stability of solutions for fast diffusion equations2010

    • Author(s)
      R. Kajikiya
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      京都大学
    • Related Report
      2012 Final Research Report
  • [Presentation] symptotic behavior of solutions of the compressible Navier-Stokes equation around a parallel flow2010

    • Author(s)
      Y. Kagei
    • Organizer
      13th International Conference on Hyperbolic Problems: Theorym Numerics, Applications
    • Place of Presentation
      Beijing, China
    • Related Report
      2012 Final Research Report
  • [Presentation] L2 boundedness of solutions for the 2D semilinear dissipative wave equations

    • Author(s)
      T. Kobayashi
    • Organizer
      RIMS研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Decay estimates of solutions to the 2D Wave equations with damping or strong damping terms

    • Author(s)
      T. Kobayashi
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] L2 boundedness for the solutions to the 2D Navies-Stokes equations

    • Author(s)
      T. Kobayashi
    • Organizer
      Parabolic and Navier-Stokes Equations 2012
    • Place of Presentation
      Banach center, Bedlewo, Poland.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 双曲型Navieer-Stokes 方程式の解のL2有界性について

    • Author(s)
      T. Kobayashi
    • Organizer
      北九州地区における偏微分方程式研究集会
    • Place of Presentation
      小倉リーセントホテル
    • Related Report
      2012 Annual Research Report
  • [Presentation] Decay estimates of solutions to the 2D exterior problems for the semilinear heat and dissipative wave equations

    • Author(s)
      T. Kobayashi
    • Organizer
      「International Workshop on Stationary Problems in Nonlinear Partial Differential Equations」
    • Place of Presentation
      Saga University
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] L2 boundedness of solutions to the 2D exterior problems for the semilinear heat equations and its applications

    • Author(s)
      T. Kobayashi
    • Organizer
      国際研究集会「量子凝集と爆発 数理物理学的視点」
    • Place of Presentation
      大阪大学基礎工学部 シグマホール
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2010-08-23   Modified: 2019-07-29  

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