The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$

Fuente: arXiv
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Auteurs principaux: An, Xinliang, Chen, Haoyang, Yin, Silu
Format: Preprint
Publié: 2022
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author An, Xinliang
Chen, Haoyang
Yin, Silu
author_facet An, Xinliang
Chen, Haoyang
Yin, Silu
contents In a fractional Sobolev space $H^s(\mathbb{R}^2)$ with $s\leq\frac74$, we prove the low-regularity ill-posedness for the 2D compressible Euler equations and the 2D ideal compressible MHD system. Our ill-posedness results match the $H^\frac74$ regularity threshold for the 2D compressible Euler system with respect to the fluid velocity and density.
format Preprint
id arxiv_https___arxiv_org_abs_2206_14003
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$
An, Xinliang
Chen, Haoyang
Yin, Silu
Analysis of PDEs
Mathematical Physics
Fluid Dynamics
In a fractional Sobolev space $H^s(\mathbb{R}^2)$ with $s\leq\frac74$, we prove the low-regularity ill-posedness for the 2D compressible Euler equations and the 2D ideal compressible MHD system. Our ill-posedness results match the $H^\frac74$ regularity threshold for the 2D compressible Euler system with respect to the fluid velocity and density.
title The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$
topic Analysis of PDEs
Mathematical Physics
Fluid Dynamics
url https://arxiv.org/abs/2206.14003