Stability theory of nonlinear waves for model systems of compressible fluid

2016 Fiscal Year Final Research Report

• Project/Area Number: 24740091
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kumamoto University (2014-2016); Kyushu University (2012-2013)
• Principal Investigator: NAKAMURA Tohru 熊本大学, 大学院先端科学研究部(工), 准教授 (90432898)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 解析学 / 偏微分方程式論 / 流体力学 / 圧縮性流体 / 漸近解析 / エネルギー法 / 粘性保存則 / 境界層解

Outline of Final Research Achievements

In the present research, we consider existence and asymptotic stability of a boundary layer solution for general symmetric systems of hyperbolic and parabolic equations. For the existence of the boundary layer solution, we show that the dimension of a local stable manifold associated with the stationary problem is given by the number of the negative characteristic speeds. For the related symmetric system of parabolic equations, we obtain the algebraic convergence rate of solutions toward the degenerate boundary layer solution. We also show that the critical value of the weight exponent is equal to 5. Concerning the result for the scalar viscous conservation laws, the result obtained in the present research is seemed to be optimal.

Free Research Field

数物系科学