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arXiv · 2305.13200

Non-uniqueness for the compressible Euler-Maxwell equations

Shunkai Mao·Peng Qu
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Abstract

We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth equilibrium-charged ion density, we could construct infinitely many $\alpha$-H\"older continuous entropy solutions emanating from the same initial data for $\alpha<\frac{1}{7}$. Especially, the electromagnetic field belongs to the H\"older class $C^{1,\alpha}$. Furthermore, we provide a continuous entropy solution satisfying the entropy inequality strictly. The proof relies on the convex integration scheme. Due to the constrain of the Maxwell equations, we propose a method of Mikado potential and construct new building blocks.

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Shunkai Mao, Peng Qu. 2023-05-22. Non-uniqueness for the compressible Euler-Maxwell equations. https://arxiv.org/abs/2305.13200

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