Long time well-posedness of compressible magnetohydrodynamics boundary layer equations in Sobolev space

Shengxin Li; Feng Xie

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arXiv · 2208.00186

Long time well-posedness of compressible magnetohydrodynamics boundary layer equations in Sobolev space

Shengxin Li·Feng Xie

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Abstract

In this paper we consider the long time well-posedness of solutions to two dimensional compressible magnetohydrodynamics (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $\varepsilon$ and the far-field state is also a small perturbation around such a steady solution in Sobolev space, then the lifespan of solutions is proved to be greater than $\varepsilon^{-\frac43}$.

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Shengxin Li, Feng Xie. 2022-07-30. Long time well-posedness of compressible magnetohydrodynamics boundary layer equations in Sobolev space. https://arxiv.org/abs/2208.00186

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