Asymptotic analysis of boundary layers for viscous compressible Navier-Stokes equatations

• Project/Area Number: 15K13449
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Kyushu University
• Principal Investigator: Kagei Yoshiyuki 九州大学, 数理学研究院, 教授 (80243913)
• Co-Investigator(Renkei-kenkyūsha): MAEKAWA Yasunori 京都大学, 理学研究科, 准教授 (70507954)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 圧縮性Navier-Stokes方程式 / 人工圧縮系 / 特異摂動 / スペクトル解析 / マッハ数 / 人口圧縮系 / スペクトル / 漸近展開 / 非圧縮極限

Outline of Final Research Achievements

The purpose of this project is to study the structure of boundary layers in limiting process of the large time behavior of solutions and the zero Mach number limit for the compressible Navier-Stokes equations. We derived the second order term of the asymptotic expansion of solutions in large time for the Cauchy problem on the whole space. We also study the spectral relations of the linearized operators around stationary solutions between the artificial compressible system and the incompressible Navier-Stokes system. It was shown that the spectrum for the artificial compressible system near the imaginary axis is decomposed into a part given by a perturbation of the spectrum for the incompressible system and a part arising from the compressible aspect of the system. We then established a sufficient condition so that a stable stationary solution of the incompressible system is also stable as a solution of the artificial compressible system.

Research Products

• [Journal Article] Asymptotic Behavior of the Linearized Semigroup at Space-Periodic Stationary Solution of the Compressible Navier-Stokes Equation (2017)
  • Author(s): Enomoto Shota、Kagei Yoshiyuki
  • Journal Title: J. Math. Fluid Mech. Volume: 19 Issue: 4 Pages: 739-772
  • DOI: 10.1007/s00021-016-0304-3
  • Peer Reviewed
• [Journal Article] Asymptotic profiles for the compressible Navier-Stokes equations on the whole space (2017)
  • Author(s): Yoshiyuki Kagei and Masatoshi Okita
  • Journal Title: J. Math. Anal. Appl. Volume: 445 Issue: 1 Pages: 297-317
  • DOI: 10.1016/j.jmaa.2016.07.024
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On Chorin's Method for Stationary Solutions of the Oberbeck-Boussinesq Equations (2016)
  • Author(s): Yoshiyuki Kagei and Takaaki Nishida
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 19 Issue: 2 Pages: 1-21
  • DOI: 10.1007/s00021-016-0284-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Large time behavior of solutions to the compressible Navier-Stokes equations in an infinite layer under slip boundary condition (2016)
  • Author(s): Abulizi Aihaiti, Shota Enomoto and Yoshiyuki Kagei
  • Journal Title: Math. Models Meth. Appl. Sci. Volume: 26 Issue: 14 Pages: 2617-2649
  • DOI: 10.1142/s0218202516500615
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Stability of time periodic solution of the Navier-Stokes equation on the half-space under oscillatory moving boundary condition (2016)
  • Author(s): Yoshiyuki Kagei and Ryouta Oomachi
  • Journal Title: J. Differential Equations Volume: 261 Issue: 6 Pages: 3366-3413
  • DOI: 10.1016/j.jde.2016.05.029
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain (2016)
  • Author(s): Reika Aoyama and Yoshiyuki Kagei
  • Journal Title: Adv. Differential Equations Volume: 21
  • Peer Reviewed
• [Journal Article] The Oberbeck-Boussinesq approximation as a constitutive limit (2015)
  • Author(s): Yoshiyuki Kagei and Michael Ruzicka
  • Journal Title: Continuum Mechanics and Thermodynamics Volume: - Issue: 5 Pages: 1411-1419
  • DOI: 10.1007/s00161-015-0483-9
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Large time behavior of solutions to the compressible Navier-Stokes equations around a parallel flow in a cylindrical domain (2015)
  • Author(s): Reika Aoyama and Yoshiyuki Kagei
  • Journal Title: Nonlinear Anal. Volume: 127 Pages: 362-396
  • DOI: 10.1016/j.na.2015.07.009
  • Peer Reviewed
• [Journal Article] Spectral properties of the linearized semigroup of the compressible Navier-Stokes equation on a periodic layer (2015)
  • Author(s): Yoshiyuki Kagei and Naoki Makio
  • Journal Title: Publ. Res. Inst. Math. Sci. Volume: 51 Issue: 2 Pages: 337-372
  • DOI: 10.4171/prims/158
  • Peer Reviewed
• [Journal Article] Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry (2015)
  • Author(s): Yoshiyuki Kagei and Kazuyuki Tsuda
  • Journal Title: J. Differential Equations Volume: 258 Issue: 2 Pages: 399-444
  • DOI: 10.1016/j.jde.2014.09.016
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Bifurcation of the compressible Taylor vortex (2018)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Seminaire de Physique Mathematique - EDP, Institute of Mathematics, University of Bordeaux, Bordeaux, France
  • Invited
• [Presentation] Stability and bifurcation analysis of the compressible Navier-Stokes equations (2018)
  • Author(s): 隠居 良行
  • Organizer: 東北大学理学部数学教室談話会
  • Invited
• [Presentation] Stability and bifurcation analysis of the compressible Navier-Stokes equations (2018)
  • Author(s): 隠居良行
  • Organizer: 第12回岩手数理科学セミナー
  • Invited
• [Presentation] Stability of space-time periodic states to the compressible Navier-Stokes equation in an infinite layer (2017)
  • Author(s): 榎本 翔太，隠居 良行，Mohamad Nor Azlan
  • Organizer: 日本数学会年会 函数方程式論分科会 一般講演
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-24
• [Presentation] Large time behavior of solutions to the compressible Navier-Stokes equations in a cylinder under the slip boundary condition (2017)
  • Author(s): アハット アブリズ，隠居 良行
  • Organizer: 日本数学会年会 函数方程式論分科会 一般講演
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-24
• [Presentation] 圧縮流体方程式の分岐・安定性解析 (I), (II) (2017)
  • Author(s): 隠居良行
  • Organizer: PDE Workshop in Miyazaki
  • Place of Presentation: 宮崎大学
  • Year and Date: 2017-01-16
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: NCTS Seminar on Applied Mathematics, National Center for Theoretical Sciences, Mathematics Division, National Taiwan University, Taipei, Taiwan
  • Invited
• [Presentation] Stability and bifurcation analysis of the compressible Navier-Stokes equations (2017)
  • Author(s): 隠居 良行
  • Organizer: 東京理科大学理工学部数学科 談話会
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: RIMS Workshop on "Theory of Evolution Equation and Mathematical Analysis of Nonlinear Phenomena", RIMS, Kyoto University
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Seminar at Shanghai Jiao Tong University
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Academic Report at School of Mathematical Sciences, Dalian University of Technology
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Seminar at Center for Partial Differential Equations and their Applications, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing
  • Invited
• [Presentation] Traveling waves bifurcating from Poiseuille fow in viscous compressible fluid (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Seminar at Capital Normal University, Beijing, China
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex I, II (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Nonlinear Partial Differential Equations for Future Applications “Hyperbolic and Dispersive PDE”, Katahira Campus, Tohoku University
  • Int'l Joint Research / Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Nonlinear PDE seminar, University Paris Diderot - Paris 7, Paris, France
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Vorticity, Rotation and Symmetry (IV) -Complexity, Regularity and Singularities, CIRM in Luminy/Marseille, France
  • Int'l Joint Research / Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): 隠居良行，西田孝明，寺本有花
  • Organizer: 日本数学会秋季総合分科会 函数方程式論分科会
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): 隠居良行
  • Organizer: 第6回岐阜数理科学研究会
  • Invited
• [Presentation] Bifurcation of the compressible Taylor vortex (2017)
  • Author(s): 隠居良行
  • Organizer: 愛媛大学解析セミナー
  • Invited
• [Presentation] Wave trains bifurcating from the Poiseuille flow of the compressible Navier-Stokes equations (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: PDE Colloquium in Konstanz
  • Place of Presentation: University of Konstanz, Konstanz, Germany
  • Invited
• [Presentation] Stability and bifurcation analysis of the compressible Navier-Stokes equations (1), (2), (3) (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: The 14th Japanese-German International Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic behavior of solutions of the compressible Navier-Stokes equations under the slip boundary condition (2017)
  • Author(s): 隠居良行
  • Organizer: 大分解析セミナー
  • Place of Presentation: 大分大学
  • Invited
• [Presentation] Stability and bifurcation analysis of the compressible Navier-Stokes equations (2017)
  • Author(s): 隠居 良行
  • Organizer: 京都大学理学部数学教室 大談話会
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Large time behavior of solutions to the compressible Navier-Stokes equations under slip boundary condition (2017)
  • Author(s): 隠居 良行
  • Organizer: 松江解析セミナー
  • Place of Presentation: 島根大学
  • Invited
• [Presentation] On the stability of stationary solutions of the artificial compressible system (2017)
  • Author(s): Yoshiyuki Kagei
  • Organizer: 第24回偏微分方程式待兼山セミナー
  • Place of Presentation: 大阪大学理学部
  • Invited
• [Presentation] 圧縮性 Navier-Stokes 方程式の Poiseuille 流の不安定性と分岐進行波解 (2016)
  • Author(s): 隠居 良行
  • Organizer: 数学協働プログラム「ワークショップ」(工学と現代数学の接点を求めて(2))
  • Place of Presentation: 大阪大学基礎工学部
  • Year and Date: 2016-12-20
  • Invited
• [Presentation] Large time behavior of solutions to the compressible Navier-Stokes equations in an infinite layer under slip boundary condition (2016)
  • Author(s): アハット アブリズ，榎本 翔太，隠居 良行
  • Organizer: 日本数学会秋季総合分科会，函数方程式論分科会 一般講演
  • Place of Presentation: 関西大学
  • Year and Date: 2016-09-15
• [Presentation] On the spectrum of linear artificial compressible system (2016)
  • Author(s): Yoshiyuki Kagei
  • Organizer: RIMS Workshop on Mathematical Analysis in Fluid and Gas Dynamics
  • Place of Presentation: Kyoto University
  • Year and Date: 2016-07-06
  • Int'l Joint Research / Invited
• [Presentation] On the artificial compressible system (2016)
  • Author(s): 隠居良行
  • Organizer: RIMS研究集会「保存則と保存則をもつ偏微分方程式に対する解の正則性，特異性および長時間挙動の研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2016-06-06
  • Invited
• [Presentation] Asymptotic profiles for the compressible Navier-Stokes equations in the whole space (2016)
  • Author(s): 沖田匡聡，隠居良行
  • Organizer: 日本数学会年会，函数方程式論分科会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-18
• [Presentation] On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation (2016)
  • Author(s): 隠居良行，西田 孝明
  • Organizer: 日本数学会年会，函数方程式論分科会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-18
• [Presentation] On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation (2016)
  • Author(s): Yoshiyuki Kagei
  • Organizer: The Navier-Stokes Equations and Related Topics
  • Place of Presentation: Nagoya University, Japan
  • Year and Date: 2016-03-09
  • Int'l Joint Research / Invited
• [Presentation] On the spectrum of linear artificial compressible system (2016)
  • Author(s): 隠居良行
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Year and Date: 2016-02-20
  • Invited
• [Presentation] On the spectrum of linear artificial compressible system (2016)
  • Author(s): 寺本有花，隠居 良行
  • Organizer: 第134回 日本数学会九州支部例会
  • Place of Presentation: 九州大学
  • Year and Date: 2016-02-13
• [Presentation] Stability of viscous compressible flows (2016)
  • Author(s): Yoshiyuki Kagei
  • Organizer: Colloquium at UNIST
  • Place of Presentation: Ulsan National Institute of Science and Technology, Korea
  • Invited
• [Presentation] On the linear artificial compressible system (2016)
  • Author(s): Yoshiyuki Kagei
  • Organizer: International Workshop on Nonlinear PDEs 2016 in Osaka
  • Place of Presentation: I-site Namba, Osaka Prefecture University
  • Int'l Joint Research / Invited
• [Presentation] On the spectrum for artificial compressible system (2016)
  • Author(s): 隠居 良行，西田 孝明，寺本 有花
  • Organizer: 日本数学会秋季総合分科会，函数方程式論分科会 一般講演
  • Place of Presentation: 関西大学
• [Presentation] On the artificial compressible system (2016)
  • Author(s): 隠居良行
  • Organizer: 岐阜数理科学セミナー
  • Place of Presentation: 岐阜大学サテライトキャンパス・多目的講義室（大）
  • Invited
• [Presentation] On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation (2015)
  • Author(s): 隠居良行
  • Organizer: 神戸大学解析セミナー
  • Place of Presentation: 神戸大学解析セミナー
  • Year and Date: 2015-12-16
  • Invited
• [Presentation] On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation (2015)
  • Author(s): 隠居良行
  • Organizer: 奈良女子大学PDEセミナー
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2015-10-27
  • Invited
• [Presentation] On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation (2015)
  • Author(s): 隠居良行
  • Organizer: 金沢解析セミナー
  • Place of Presentation: 金沢大学
  • Year and Date: 2015-10-23
  • Invited
• [Presentation] On Chorin's method for stationary solutions of the incompressible Navier-Stokes equation (2015)
  • Author(s): 隠居良行
  • Organizer: 非線形解析セミナー
  • Place of Presentation: 慶應義塾大学理工学部
  • Year and Date: 2015-08-03
  • Invited
• [Funded Workshop] The 35th Kyushu Symposium on Partial Differential Equations (2018)
• [Funded Workshop] German-Japanese Workshop on Partial Differential Equations (2017)
  • Place of Presentation: University of Konstanz, Konstanz, Germany
  • Year and Date: 2017-03-15
• [Funded Workshop] The 34th Kyushu Symposium on Partial Differential Equations (2017)
  • Place of Presentation: Kyushu University Nishijin Plaza
  • Year and Date: 2017-01-30
• [Funded Workshop] Ito Workshop on Partial Differential Equations (2017)
• [Funded Workshop] The 33rd Kyushu Symposium on Partial Differential Equations (2016)
  • Place of Presentation: Kyushu University Nishijin Plaza
  • Year and Date: 2016-01-27