Analysis of stablity and bifurcation for compressible fluid equations
| Project/Area Number |
24340028
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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 九州大学, 数理(科)学研究科(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)
KOBAYASHI Takayuki 大阪大学, 基礎工学研究科, 教授 (50272133)
NAKAMURA Tohru 熊本大学, 自然科学研究科, 准教授 (90432898)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | Navier-Stokes equation / compressible / asymptotic behavior / spectral anaylsis / stability / instability / bifurcation / 圧縮性Navier-Stokes方程式 / ポワズイユ流 / 不安定 / 分岐 / 進行波解 / 非圧縮性Navier-Stokes方程式 / 時間周期解 / 空間周期解 / 安定性 / スペクトル解析 / 漸近挙動 / スペクトル |
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| Outline of Final Research Achievements |
To establish mathematical theory for bifurcation and stability in the compressible Navier-Stokes equation, we studied the stability of stationary and time-periodic parallel flows. We proved that the asymptotic behavior of parallel flow is described by a linear heat equation when the space dimension n is greater than or equal to 3, and by a one-dimensional viscous Burgers equation when n=2. In the case of the Poiseuille flow, we derived a sufficient condition for the instability in terms of the Reynolds and Mach numbers. Furhtermore, we proved the bifurcation of a familiy of space-time-peirodic traveling waves when the Poiseuille flow is getting unstable. As a first step of the stability analysis of space-periodic patterns, we investigate the stablity of the motionless state on periodic infinte layer, and derived the asymptotic leading part of the perturbation by using the Bloch transformation.
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Report
(5 results)
Research Products
(140 results)
