2017 Fiscal Year Final Research Report
Asymptotic analysis of boundary layers for viscous compressible Navier-Stokes equatations
| Project/Area Number |
15K13449
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MAEKAWA Yasunori 京都大学, 理学研究科, 准教授 (70507954)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 圧縮性Navier-Stokes方程式 / 人工圧縮系 / 特異摂動 / スペクトル解析 / マッハ数 |
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| Outline of Final Research Achievements |
The purpose of this project is to study the structure of boundary layers in limiting process of the large time behavior of solutions and the zero Mach number limit for the compressible Navier-Stokes equations. We derived the second order term of the asymptotic expansion of solutions in large time for the Cauchy problem on the whole space. We also study the spectral relations of the linearized operators around stationary solutions between the artificial compressible system and the incompressible Navier-Stokes system. It was shown that the spectrum for the artificial compressible system near the imaginary axis is decomposed into a part given by a perturbation of the spectrum for the incompressible system and a part arising from the compressible aspect of the system. We then established a sufficient condition so that a stable stationary solution of the incompressible system is also stable as a solution of the artificial compressible system.
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| Free Research Field |
偏微分方程式論
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