Sobolev空间中可压缩磁流体边界层方程的长时间适定性

IF 1.1 3区数学 Q1 MATHEMATICS

Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI:10.3934/dcds.2023133

Shengxin Li, Feng Xie

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引用次数: 0

摘要

本文考虑二维可压缩磁流体边界层方程解的长时间适定性。当初始数据是大小为$ \varepsilon $的稳定解的小扰动时，则证明了Sobolev空间中解的寿命大于$ \varepsilon^{-\frac43} $。这一结果可以推广到初始数据和远场状态都是围绕稳态的小扰动的情况。此外，它对等熵和非等熵磁流体边界层方程都成立。

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Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces

In this paper we consider the long time well-posedness of solutions to two-dimensional compressible magnetohydrodynamic (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $ \varepsilon $, then the lifespan of solutions in Sobolev spaces is proved to be greater than $ \varepsilon^{-\frac43} $. And such a result can be extended to the case that both initial data and far-field state are small perturbations around the steady states. Moreover, it holds true for both isentropic and non-isentropic magnetohydrodynamic boundary layer equations.

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来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.