2016 Fiscal Year Final Research Report
Toward a global analysis for nonlinear partial differential equations
| Project/Area Number |
26400163
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Research Collaborator |
TERAMOTO Yoshiaki 摂南大学, 教授
KAGEI Yoshiyuki 九州大学, 教授
Padula Mariarosaria Professor of Ferrara University
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 関数方程式 / 解析学 / 非線形偏微分方程式系 / 大域的解析 / 計算機援用解析 / 流体方程式系 |
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| Outline of Final Research Achievements |
1. Heat convection problems of compressible and viscous fluids in the horizontal strip domain under the gravity heated from below. We have analyzed stationary bifurcations and its time evolutions while we notice an important parameter L which depends inversely on the temperature gradient and the depth of the domain. When the parameter L tends to the infinity, we analyzed how the solutions of the system converge to those of the incompressible Oberbeck-Boussinesq system.
2. We analyzed the stability of the compressible Poiseuille flow. When the Mach number is not small, the flow becomes unstable with a much smaller Reynold number compared with the critical Reynold number for the incompressible Poiseuille flow.
3. As a justification of an 'artificial compressible' perturbation to the incompressible viscous fluids, we analyzed the stability of the stationary bifurcated solutions of the heat convection problems.
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| Free Research Field |
数物系科学
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