Regularity and uniqueness for the 3D compressible magnetohydrodynamic equations

Boundary Value Problems

Mingyu Zhang¹ 

[1] School of Mathematics and Information Science, Weifang University;

关键词: Compressible magnetohydrodynamic equations;    Cauchy problem;    Strong solutions;    Global existence;    Uniqueness;   

DOI  :  10.1186/s13661-022-01593-2

来源: DOAJ

【 摘 要 】

Abstract In this paper, some new L p $L^{p}$ gradient estimates are justified for the three-dimensional compressible magnetohydrodynamic equations in the whole space R 3 $\mathbb{R}^{3}$ . The key to derive the estimate ∥ ∇ u ∥ L 3 $\|\nabla \textbf {u}\|_{L^{3}}$ is the “div-curl” decomposition technique. For regular initial data with small energy, we prove the existence of global solutions belonging to a new class of functions in which the uniqueness can be shown to hold.

【 授权许可】

Unknown