Large-time behavior of motion for compressible viscous fluid in unbounded domain

• Project/Area Number: 19840037
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: NAKAMURA Tohru Kyushu University, 大学院・数理学研究院, 助教 (90432898)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,756,000 (Direct Cost: ¥2,390,000、Indirect Cost: ¥366,000); Fiscal Year 2008: ¥1,586,000 (Direct Cost: ¥1,220,000、Indirect Cost: ¥366,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥1,170,000)
• Keywords: 解析学 / 関数方程式 / 圧縮性流体 / 漸近解析 / エネルギー法 / 粘性保存則 / 境界層解 / 関数方程式論 / 流体

Research Abstract

本研究では,圧縮性粘性流体のモデル方程式として知られる圧縮性Navier-Stokes方程式の解の時間漸近挙動に関する研究を行った.具体的には,1次元及び多次元半空間領域における等エントロピーモデルに対する流出(Outflow)問題を考察し,解の定常解への漸近率の算出に成功した.本研究で得られた漸近率は,松村・川島・西原等による単独粘性保存則に対する結果を鑑みると,ほぼ最適であると予想される.

Research Products

• [Journal Article] Stability of planar stationary waves for damped wave equations with nonlinear con-vection in multi-dimensional half space (2008)
  • Author(s): Y.Ueda, T.Nakamura and S.Kawashima
  • Journal Title: Kinetic and Related Models 1, no.1 Pages: 49-64
  • Peer Reviewed
• [Journal Article] Large-time behavior of spherically symmetric ow of heat-conductive gas in a eld of potential forces (2008)
  • Author(s): T.Nakamura and S.Nishibata
  • Journal Title: Indiana Univ. Math. J. 57, no.2 Pages: 1019-1054
  • Peer Reviewed
• [Journal Article] Half space problem for the compressible Navier-Stokes equation (2008)
  • Author(s): T.Nakamura and S.Nishibata
  • Journal Title: to appear in Proceedings of Hyp
  • Peer Reviewed
• [Journal Article] Large-time behavior of spherically symmetric flow of heat-con ductive gas in a field of potential forces (2008)
  • Author(s): T. Nakamura, et al
  • Journal Title: Indiana Univ. Math. J. 57 Pages: 1019-1054
  • Peer Reviewed
• [Journal Article] Convergence rate of solutions toward sta-tionary solutions to the compressible Navier-Stokes equation in a half line (2007)
  • Author(s): T.Nakamura, S.Nishibata and T.Yuge
  • Journal Title: J. Differential Equations 241, no.1 Pages: 94-111
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of spherically symmetric ow for vis-cous heat-conductive gas (2007)
  • Author(s): T.Nakamura and S.Nishibata
  • Journal Title: Nonlinear Analysis and Convex Analysis Pages: 451-459
  • Peer Reviewed
• [Journal Article] Large-time behavior of solutions for the com-pressible viscous uid in a half space (2007)
  • Author(s): T.Nakamura, S.Nishibata and T.Yuge
  • Journal Title: 京都大学数理解析研究所講究録 1536 Pages: 122-131
• [Journal Article] Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line (2007)
  • Author(s): T. Nakamura, et. al.
  • Journal Title: J.Differential Equations 241 Pages: 94-111
  • Peer Reviewed
• [Journal Article] Stability of degenerate stationary waves for viscous gases
  • Author(s): Y.Ueda, T.Nakamura and S.Kawashima
  • Journal Title: to appear in Archive for Rational Mechanics and Analysis
  • Peer Reviewed
• [Journal Article] Half space problem for the compressible Navier-Stokes equation
  • Author(s): T. Nakamura, et al
  • Journal Title: to appear in Proceedings of Hyp2008 (掲載決定)
  • Peer Reviewed
• [Presentation] Stationary waves for viscous heat-conductive uid in half space (2009)
  • Author(s): T.Nakamura
  • Organizer: The Sixth International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-03-28
• [Presentation] 1次元半空間における熱伝導圧縮性粘性流体の定常波について (2009)
  • Author(s): 中村徹
  • Organizer: 若手による流体力学の基礎方程式の研究集会
  • Place of Presentation: 名古屋大
  • Year and Date: 2009-03-10
• [Presentation] Stationary wave for com-pressible viscous and heat-conductive uid in half space (2009)
  • Author(s): T.Nakamura
  • Organizer: 第26回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2009-01-28
• [Presentation] 圧縮性Navier-Stokes方程式に対する定常解の安定性解析 (2008)
  • Author(s): 中村徹
  • Organizer: 第3回奈良偏微分方程式研究会
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2008-12-13
• [Presentation] Existence and stability of stationary waves for viscous heat-conductive uid in half space (2008)
  • Author(s): T.Nakamura
  • Organizer: First China-Japan Workshop on Mathematical Topics from Fluid Mechanics Chinese Academy of Sciences
  • Place of Presentation: Beijing, China
  • Year and Date: 2008-11-11
• [Presentation] 1次元半空間における圧縮性粘性流体の理想気体モデルの解の時間漸近挙動 (2008)
  • Author(s): 中村徹
  • Organizer: 偏微分方程式の諸問題
  • Place of Presentation: 東海大学
  • Year and Date: 2008-11-01
• [Presentation] 半直線上の熱伝導圧縮性粘性流体の定常解について (2008)
  • Author(s): 中村徹, 西畑伸也, 川島秀一, P.C.Zhu
  • Organizer: 日本数学会2008年度秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-26
• [Presentation] Large time behavior of solu-tions to viscous heat-conductive gases in half space (2008)
  • Author(s): T.Nakamura
  • Organizer: 12th International Conference on Hyperbolic Problems : Theory, Numerics, Applications, University of Maryland
  • Place of Presentation: College Park, U.S.A.
  • Year and Date: 2008-06-10
• [Presentation] Large time behavior of solutions to viscous heat-conductive gases in half space (2008)
  • Author(s): T. Nakamura
  • Organizer: 12th International Conference on Hyperbolic Problems
  • Place of Presentation: メリーランド大学
  • Year and Date: 2008-06-10
• [Presentation] Asymptotic stability of stationary waves for compressible viscous uid in half space (2008)
  • Author(s): 中村徹
  • Organizer: 偏微分方程式待兼山セミナーNo.16
  • Place of Presentation: 大阪大学
  • Year and Date: 2008-02-05
• [Presentation] Asymptotic behavior of so-lutions for compressible viscous uid in half space (2008)
  • Author(s): T.Nakamura
  • Organizer: Nonlinear Wave and Dispersive Equations
  • Place of Presentation: 京都大学
  • Year and Date: 2008-01-22
• [Presentation] Stability of stationary waves for compressible viscous uid in multi-dimensional half space (2008)
  • Author(s): 中村徹
  • Organizer: 若手による流体力学の基礎方程式の研究集会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2008-01-06
• [Presentation] 多次元半空間における圧縮性粘性流体の縮退定常波の漸近安定性 (2007)
  • Author(s): 中村徹, 西畑伸也
  • Organizer: 日本数学会2007年度秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] 多次元半空間における圧縮性粘性流体の縮退定常波の漸近委定性 (2007)
  • Author(s): 中村 徹, 西畑 伸也
  • Organizer: 日本数学会2007年度秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] Half space problem for the compressible Navier-Stokes equation (2007)
  • Author(s): T.Nakamura
  • Organizer: 第三回流体と保存則の研究集会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2007-09-13