Asymptotic structure of the solutions to the system of compressible fluid

• Project/Area Number: 19540191
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Saga University
• Principal Investigator: KOBAYASHI Takayuki Saga University, 理工学部, 教授 (50272133)
• Co-Investigator(Kenkyū-buntansha): KAGEI Yoshiyuki 九州大学, 大学院・数理学研究院, 教授 (80243913) ; IKEHATA Ryo 広島大学, 教育学研究科, 准教授 (10249758)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 関数方程式 / 圧縮性流体 / 圧縮性Navier-Stokes方程式

Research Abstract

We consider the Navier-Stokes-Poisson equation describing the motion of compressible viscous isentropic gas flow under the self-gravitational force. We proved the existence of finite energy weak solutions in three dimensional bounded domain and discussed the stability of equilibrium. Also, we consider the equations to the Magneto-Hydrodynamics, and proved the existence of weak solutions.

Research Products

• [Journal Article] Weak solutions to the Navier-Stokes equation (2008)
  • Author(s): T. Kobayashi, T. Suzuki
  • Journal Title: Advances in Differential Equations. Number18ofVolume1 Pages: 141-168
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain (2008)
  • Author(s): Y. Kagei, T. Nukumizu
  • Journal Title: Osaka J. Math. vol.45 Pages: 987-1026
  • NAID: 120005986695
  • Peer Reviewed
• [Journal Article] Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer (2008)
  • Author(s): Y. Kagei
  • Journal Title: Hiroshima Math. J. vol.38 Pages: 95-124
  • Peer Reviewed
• [Journal Article] Global existence of weak solutions for 2-D semilinear wave equationswith strong damping in an exterior domain (2008)
  • Author(s): R. Ikehata, Y. Inoue
  • Journal Title: Nonlinear Anal. 68.No.1 Pages: 154-169
  • Peer Reviewed
• [Journal Article] Weak solutions to the Navier-Stokes-Poisson equation (2008)
  • Author(s): T. Kobayashi, T. Suzuki
  • Journal Title: Advances in Mathematical Sciences and Applications Number 18 Vol 1 Pages: 141-168
  • Peer Reviewed
• [Journal Article] Weak solutions to the Navier-Stokes-Poisson equation (2008)
  • Author(s): T.Kobayashi and T.Suzuki
  • Journal Title: Advances in Mathematical Sciences and Applications Number 18 of Volumel(to appear)
  • Peer Reviewed
• [Journal Article] Global existence of weak solutions for 2-D semilinear wave equationswith strong damping in an exterior domain (2008)
  • Author(s): R.Ikehata and Y.Inoue
  • Journal Title: Nonlinear Anal. 68.No.1 Pages: 154-169
  • Peer Reviewed
• [Journal Article] Weak solutions to the equations of Magnet-Hydrodynamics (2007)
  • Author(s): T. Kobayashi, T. Suzuki
  • Journal Title: Proceedings of the National Institute for Mathematical Sciences. Vol.2 Pages: 175-180
• [Journal Article] Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer (2007)
  • Author(s): Y. Kagei
  • Journal Title: Publ. Res. Inst. Math. Sci. vol.43 Pages: 763-794
  • NAID: 110006385905
  • Peer Reviewed
• [Journal Article] Resolvent estimates for the linearized compressible Navier-Stokes equation in an infinite layer (2007)
  • Author(s): Y. Kagei
  • Journal Title: Funkcial. Ekvac. vol.50 Pages: 287-337
  • NAID: 130000140689
  • Peer Reviewed
• [Journal Article] Local energy decay for linear hyperbolic equations with initial data decaying slowly near infinity (2007)
  • Author(s): R. Ikehata, G. Sobukawa
  • Journal Title: Hokkaido Math. J. 36No.1 Pages: 53-71
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer (2007)
  • Author(s): Y.Kagei
  • Journal Title: Publ. Res. Inst. Math. Sci vol.43 Pages: 763-794
  • NAID: 110006385905
  • Peer Reviewed
• [Journal Article] Resolvent estimates for the linearized compressible Navier-Stokes equation in an infinite layer (2007)
  • Author(s): Y.Kagei
  • Journal Title: Funkcial. Ekvac Vol.50 Pages: 287-337
  • NAID: 130000140689
  • Peer Reviewed
• [Journal Article] Local energy decay for linear hyperbolic equations with initial data decaying slowly near infinity (2007)
  • Author(s): R.Ikehata and G.Sobukawa
  • Journal Title: Hokkaido Math.J. 36.No.1 Pages: 53-71
  • Peer Reviewed
• [Presentation] Weak solutions to some equations of the compressible viscous flow (2009)
  • Author(s): T. Kobayashi
  • Organizer: Linear and Nonlinear Waves
  • Place of Presentation: 滋賀県立県民交流センター
  • Year and Date: 2009-11-05
• [Presentation] Weak solutions to some equations of the compressible viscous flow (2009)
  • Author(s): Takayuki KOBAYASHI
  • Organizer: Linear and Nonlinear Waves, No.7
  • Place of Presentation: 滋賀県立県民交流センター
  • Year and Date: 2009-11-05
• [Presentation] 外部領域におけるNavier-Stokes方程式の解の重み付き評価について (2009)
  • Author(s): 小林孝行
  • Organizer: 第57回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 2009-06-11
• [Presentation] 外部領域におけるStokes半群の重み付きLp-Lq評価について (2008)
  • Author(s): 小林孝行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-27
• [Presentation] 外部領域におけるStokes半群の重み付きLp-Lq 評価について (2008)
  • Author(s): 小林孝行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-27
• [Presentation] 非有界領域上の双曲型方程式のエネルギー減衰 (2008)
  • Author(s): 池畠良
  • Organizer: 研究集会「第四回非線型の諸問題」
  • Place of Presentation: 佐賀大学
  • Year and Date: 2008-09-22
• [Presentation] Fluid mechanical approximation to the degenerated drift-diffusion system from compressible Navier-Stokes- Poisson system (2008)
  • Author(s): T. Kobayashi
  • Organizer: Mathematical Fluid Dynamics
  • Place of Presentation: Darmstadt Germany
  • Year and Date: 2008-09-10
• [Presentation] Fluid mechanical approximation to the degenerated drift-diffusion system from compressible Navier-Stokes-Poisson system (2008)
  • Author(s): Takayuki KOBAYASHI
  • Organizer: Mathematical Fluid Dynamics
  • Place of Presentation: Darmstadt Germany
  • Year and Date: 2008-09-10
• [Presentation] Weighted estimates for the Stokes semig roup in an exterior Domain (2008)
  • Author(s): T. Kobayashi
  • Organizer: Parabolic and Navier Stokes
  • Place of Presentation: Banach Center、Poland
  • Year and Date: 2008-09-02
• [Presentation] Weighted estimates for the Stokes semigroup in an exterior domain (2008)
  • Author(s): Takayuki KOBAYASHI
  • Organizer: Parabolic and Navier Stokes 2008
  • Place of Presentation: Banach Center、Poland
  • Year and Date: 2008-09-02
• [Presentation] Fluid mechanical approximation to the degenerated drift-diffusion system from compressible Navier-Stokes-Poisson system (2008)
  • Author(s): T. Kobayashi
  • Organizer: New Aspects and Development of Mathematical Analysis in Nonlinear Phenomena
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2008-05-29
• [Presentation] Fluid mechanical approximation to the degenerated drift-diffusion system from compressible Navier-Stokes-Poisson system (2008)
  • Author(s): Takayuki Kobayashi
  • Organizer: New Aspects and Development of Mathematical Analysis in Nonlinear Phenomena
  • Place of Presentation: 九州大学 西新プラザ
  • Year and Date: 2008-05-29
• [Presentation] On asymptotic behavior of solutions to the compressible Navier-Stokes equation around the plane Couette flow (2008)
  • Author(s): Y. Kagei
  • Organizer: First China-Japan Workshop on MathematicalTopics from Fluid Mechanics
  • Place of Presentation: Beijing, China
• [Presentation] On the stability of the plane Couette flow of the compressible Navier-Stokes equation (2008)
  • Author(s): Y. Kagei
  • Organizer: Mathematical Fluid Dynamics
  • Place of Presentation: Darmstadt, Germany
• [Presentation] Fluid Mechanical Approximation to the Degenerated Drift-DiffusionSystem from Barotoropic Compressible Naveier-Stokes-Poisson system (2007)
  • Author(s): T. Kobayashi
  • Organizer: Analysis Seminar
  • Place of Presentation: 中国北京応用物理計算数学研究所
  • Year and Date: 2007-11-23
• [Presentation] Asymptotic behavior of solutions to the compressible Navier-Stokes equations in an infinite layer : Stability of the motionless state and the plane Couette flow (2007)
  • Author(s): Y. Kagei
  • Organizer: Analysis Seminar, Institute of Applied Physics and Computational Mathematics
  • Place of Presentation: Beijing, China
  • Year and Date: 2007-11-23
• [Presentation] Fluid Mechanical Approximation to the Degenerated Dxift-DiffusionSystem from Barotoropic Compressible Naveier-Stokes-Poisson system (2007)
  • Author(s): T.Kobayashi
  • Organizer: Analysis Seminar
  • Place of Presentation: 中国北京 応用物理計算数学研究所
  • Year and Date: 2007-11-23
• [Presentation] Asymptotic behavior of solutions to the compressible Navier-Stokes equations in an infinite layer: Stability of the motionless state and the plane Couette flow, (2007)
  • Author(s): Y.Kagei
  • Organizer: Analysis Seminar
  • Place of Presentation: 中国北京 応用物理計算数学研究所
  • Year and Date: 2007-11-23
• [Presentation] 圧縮性Navier-Stokes-Poisson方程式の緩和時間0極限と退化drift-diffusion方程式 (2007)
  • Author(s): 小林孝行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] 圧縮性Navier-Stokes-Poisson方程式の緩和時間 0 極限と退化 drift-diffusion 方程式 (2007)
  • Author(s): 小林 孝行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] Asymptotic behavior of solutions to the compressible Navier- Stokes equations in an infinite layer : Stability of the motionless state and the plane Couette flow (2007)
  • Author(s): Y. Kagei
  • Organizer: Seminar at MIP
  • Place of Presentation: University of Paul Sabatier, Toulouse, France
  • Year and Date: 2007-09-17
• [Presentation] Weak solution to the equations for the Magneto-Hydrodynamics (2007)
  • Author(s): T. Kobayashi
  • Organizer: NIMS International Workshop on Fluid Dynamics
  • Place of Presentation: NIMS, Daejeon, Korea
  • Year and Date: 2007-06-11
• [Presentation] Weak solution to the equations for the Magneto-Hydrodynamics (2007)
  • Author(s): T.Kobayashi
  • Organizer: NIMS International Workshop on Fluid Dynamics
  • Place of Presentation: NIMS, Daejeon, Korea.
  • Year and Date: 2007-06-11
• [Presentation] Asymptotic behavior of solutions to the compressible Navier-Stokes equations in an infinite layer: Stability of the motionless state and the plane Couette flow (2007)
  • Author(s): Y.Kagei
  • Organizer: Seminar at MIP
  • Place of Presentation: University of Paul Sabatier, Toulouse, France