Diffusion wave property of the solutions to the system of the viscous fluid flow

• Project/Area Number: 25400175
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka University
• Principal Investigator: Takayuki Kobayashi 大阪大学, 基礎工学研究科, 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) ; KUBO TAKAYUKI 筑波大学, 数理物質科学研究科, 講師 (90424811)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 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

Outline of Final Research Achievements

We consider the initial boundary value problems for incompressible Navier-Stokes equations in half space and perturbed half space. We proved the time decay estimates for the solutions in weighted Lp space. We also consider the semilinear heat equations and dissipative wave equations in two dimension exterior domains. We showed the L2 boundedness with respect to the space and time valuables of the solutions for initial data in the Hardy space.

Research Products

• [Journal Article] Weighted Lp － Lq Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations (2016)
  • Author(s): T. Kobayashi and T. Kubo
  • Journal Title: Recent Developments of Mathematical Fluid Mechanics, Advances in Mathematical Fluid Mechanics Volume: なし Pages: 337-349
  • DOI: 10.1007/978-3-0348-0939-9_18
  • ISBN: 9783034809382, 9783034809399
  • Peer Reviewed / Open Access
• [Journal Article] L2 boundedness of the solutions to the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equations (2015)
  • Author(s): T. Kobayashi
  • Journal Title: RIMS kokyuroku. Volume: 1971 Pages: 69-75
• [Journal Article] Weighted estimate of Stokes semigroup in unbounded domains. (2014)
  • Author(s): T. Kobayashi and T. Kubo
  • Journal Title: Advanced Studies in Pure Mathematics Volume: 64 Pages: 427-435
  • Peer Reviewed
• [Journal Article] Three positive solutions of the one-dimensional generalized Henon equation. (2014)
  • Author(s): R. Kajikiya
  • Journal Title: Results in Mathematics Volume: 66 Issue: 3-4 Pages: 427-459
  • DOI: 10.1007/s00025-014-0385-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Weighted Lp-Lq estimates of the Stokes semigroup in some unbounded domains equations (2013)
  • Author(s): T. Kobayashi and T. Kubo
  • Journal Title: Tsukuba Journal of Mathematics Volume: 37. No.2 Pages: 179-205
  • Peer Reviewed
• [Journal Article] L2 boundedness for the 2D exterior problems for the semilinear heat and dissipative wave equations (2013)
  • Author(s): T. Kobayashi and M. Misawa
  • Journal Title: Rims Kokyuroku Bessatsu Volume: B42 Pages: 1-11
  • Peer Reviewed
• [Journal Article] Fluid Mechanical Approximation to the Degenerated Drift-Diffusion System from Compressible Navier-Stokes-Poisson system (2013)
  • Author(s): T. Kobayashi and T. Ogawa
  • Journal Title: Indiana Univ. Math. J. Volume: 62. No. 3. Pages: 1021-1054
  • NAID: 130004604066
  • Peer Reviewed
• [Journal Article] Least energy solutions and group invariant solutions of the Henon equation. (2013)
  • Author(s): R. Kajikiya
  • Journal Title: Advanced Nonlinear Studies Volume: 13. No.3 Pages: 721-738
  • Peer Reviewed
• [Presentation] 圧縮性Navier-Stokes方程式の解の漸近挙動 (2016)
  • Author(s): 小林孝行
  • Organizer: 応用非線形偏微分方程式論の展開
  • Place of Presentation: 大阪府豊中市 大阪大学基礎工学研究科
  • Year and Date: 2016-03-27
• [Presentation] Decay estimates of the solutions to the 2D compressible Navier-Stokes equation (2016)
  • Author(s): T. Kobayashi
  • Organizer: The Navier-Stokes Equations and Related Topics
  • Place of Presentation: 愛知県名古屋市, 名古屋大学大学院多元数理科学研究科
  • Year and Date: 2016-03-07
  • Invited
• [Presentation] ２次元圧縮性 Navier-Stokes 方程式の解の漸近挙動について (2015)
  • 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: 福岡県北九州市 ,小倉リーセントホテル
  • Year and Date: 2015-11-28
• [Presentation] Decay estimates of the solutions to the 2D linear viscoelastic equations and its applications to the compressible Navier-Stokes equations (2015)
  • Author(s): T. Kobayashi
  • Organizer: International Workshop on the Multi-Phase Flow; Analysis, Modeling and Numerics
  • Place of Presentation: Nishi-Waseda Campus, Waseda University, Tokyo
  • Year and Date: 2015-11-10
  • Invited
• [Presentation] L2-boundedness of the solutions to the 2D compressible Navier-Stokes equations (2015)
  • Author(s): T. Kobayashi
  • Organizer: Mathflows 2015
  • Place of Presentation: The IGESA center，Porquerolles, France
  • Year and Date: 2015-09-13
  • Invited
• [Presentation] Decay property for the 2D Hyperbolic Navier-Stokes equations and its applications (2014)
  • Author(s): 小林孝行
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学理学部(京都府左京区)
  • Year and Date: 2014-12-20 – 2014-12-21
  • Invited
• [Presentation] Decay estimates of solutions to the 2D dissipative wave equations and Hyperbolic Navier-Stokes equations (2014)
  • Author(s): T. Kobayashi
  • Organizer: 研究集会「International Conference on Recent Advances in Hyperbolic Partial Differential Equations」
  • Place of Presentation: 広島国際会議場(広島県広島市)
  • Year and Date: 2014-12-04 – 2014-12-06
  • Invited
• [Presentation] L2 boundedness of the solutions to the 2D Navier-Stokes equations and Hyperbolic Navier-Stokes equations (2014)
  • Author(s): T. Kobayashi
  • Organizer: RIMS研究集会「非圧縮性粘性流体の数理解析」
  • Place of Presentation: 京都大学数理解析研究所(京都府左京区)
  • Year and Date: 2014-11-17 – 2014-11-19
  • Invited
• [Presentation] Decay estimates of the solutions to the 2D Hyperbolic Navier-Stokes equations. (2014)
  • Author(s): T. Kobayashi
  • Organizer: Wayamba International Conference 2014
  • Place of Presentation: Wayamba University of Sri Lanka, Kuliyapitiya, Sri Lanka
  • Year and Date: 2014-08-29 – 2014-08-30
  • Invited
• [Presentation] Decay estimates of solutions to the 2D Hyperbolic Navier-Stokes equations and its applications. (2014)
  • Author(s): T. Kobayashi
  • Organizer: 2014 ICM-Satellite-Cau “Mathematical Theorey of Gases and Fluids and Related Applications”
  • Place of Presentation: Chung-Ang University, Seoul, Korea
  • Year and Date: 2014-08-10 – 2014-08-12
  • Invited
• [Presentation] L2 boundedness of the solutions to the 2D linear viscoelastic equations and its applications (2014)
  • Author(s): 小林孝行
  • Organizer: NLPDEセミナー
  • Place of Presentation: 京都大学理学部(京都府左京区)
  • Year and Date: 2014-05-16
  • Invited
• [Presentation] ２次元双曲型 Navier-Stokes 方程式の解の L2 有界性 (2014)
  • Author(s): 小林孝行
  • Organizer: 南大阪応用数学セミナー
  • Place of Presentation: 大阪府立大学中百舌鳥キャンパス(大阪府堺市)
  • Year and Date: 2014-04-26
  • Invited
• [Presentation] ２次元線形粘性弾性体方程式 と２次元 Navier-Stokes 方程式の解の L2 有界性 (2014)
  • Author(s): 小林孝行
  • Organizer: 大阪大学数学教室 微分方程式セミナー
  • Place of Presentation: 大阪大学理学部(大阪府豊中市)
  • Year and Date: 2014-04-25
  • Invited
• [Presentation] L2 boundedness of the solutions to the 2D heat equations and the 2D Navier-Stokes equations. (2013)
  • Author(s): T. Kobayashi
  • Organizer: Analysis Seminar, Pisa
  • Place of Presentation: Pisa University, Pisa, Italy
  • Invited
• [Presentation] L2 boundedness of solutions to the 2D exterior problems for the semilinear heat and dissipative wave equations (2013)
  • Author(s): T. Kobayashi
  • Organizer: 9th International Isaac congress
  • Place of Presentation: Pedagogical University, Krakow, Poland
  • Invited
• [Presentation] L2 boundedness of solutions to the 2D dissipative wave equations (2013)
  • Author(s): T. Kobayashi
  • Organizer: Nonlinear Wave Equations and Fluid Mechanics
  • Place of Presentation: 室蘭工業大学数学ゼミナール室（北海道室蘭市）
  • Invited
• [Presentation] L2 boundedness of the solutions to the 2D Hyperbolic Navier-Stokes equations (2013)
  • Author(s): T. Kobayashi
  • Organizer: Mathematical Analysis of Nonlinear Partial Differential Equations
  • Place of Presentation: 九州大学西新プラ ザ（福岡市福岡市早良区）
  • Invited
• [Presentation] Decay estimates of solutions to the 2D heat equations and its applications
  • Author(s): 小林孝行
  • Organizer: 神戸大解析セミナー
  • Place of Presentation: 神戸大学理学部（兵庫県神戸市灘区）)
  • Invited
• [Presentation] Decay estimates of solutions to the 2D dissipative wave equations
  • Author(s): 小林孝行
  • Organizer: 金沢解析セミナー
  • Place of Presentation: 金沢大学コロキウム3（石川県金沢市）
  • Invited
• [Presentation] L2 boundedness for the solutions to the 2D damped or strong damped wave equations
  • Author(s): 小林孝行
  • Organizer: 三大学偏微分方程式セミナー
  • Place of Presentation: 中央大学後楽園キャンパス（東京都文京区）
  • Invited
• [Presentation] ２次元波動方程式の解の有界性と圧縮性流体への応用
  • 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: KMMビル（福岡県北九 州市小倉北区）
• [Book] The Proceedings on Mathematical Fluid Dynamics and nonlinear Wave (2015)
  • Author(s): T. Kobayashi, S. Shimizu, Y. Enomoto, N. Yamaguchi, T. Kubo
  • Total Pages: 192
  • Publisher: Gakkotosho Tokyo Japan