2009 Fiscal Year Final Research Report
Asymptotic analysis of systems of nonlinear partial differential equations describing motions of viscous fluids
| Project/Area Number |
19340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
KAGEI Yoshiyuki Kyushu University, 大学院・数理研究院, 教授 (80243913)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHIMA Shuichi 九州大学, 大学院・数理研究院, 教授 (70144631)
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| Co-Investigator(Renkei-kenkyūsha) |
OGAWA Takayoshi 東北大学, 大学院・理学研究科, 教授 (20224107)
KOBAYASHI Takayuki 佐賀大学, 理工学部, 教授 (50272133)
IGUCHI Tatsuo 慶応義塾大学, 理工学部, 准教授 (20294879)
NAKAMURA Tohru 九州大学, 大学院・数理学研究院, 助教 (90432898)
MAEKAWA Yasunori 神戸大学, 理学研究科, 講師 (70507954)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 圧縮性Navier-Stokes方程式 / 安定性 / 漸近挙動 |
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| Research Abstract |
We studied the asymptotic behavior of solutions of the compressible Navier-Stokes equation which describes motion of viscous fluids. We analyzed the stability properties of stationary solutions such as the motionless state and parallel flows in detail. It was proved that these stationary solutions are asymptotically stable if they are small enough in some sense. Furthermore, it was shown that the disturbances behave like solutions of convective heat equations in large time.
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