Translator Disclaimer
June, 2020 Singularity Formation of the Non-barotropic Compressible Magnetohydrodynamic Equations Without Heat Conductivity
Xin Zhong
Taiwanese J. Math. 24(3): 603-628 (June, 2020). DOI: 10.11650/tjm/190701

Abstract

We study the singularity formation of strong solutions to the three-dimensional full compressible magnetohydrodynamic equations with zero heat conduction in a bounded domain. We show that for the initial density allowing vacuum, the strong solution exists globally if the density $\rho$, the magnetic field $\mathbf{b}$, and the pressure $P$ satisfy $\|\rho\|_{L^{\infty}(0,T;L^{\infty})} + \|\mathbf{b}\|_{L^{\infty}(0,T;L^6)} + \|P\|_{L^{\infty}(0,T;L^{\infty})} \lt \infty$ and the coefficients of viscosity verity $3\mu \gt \lambda$. This extends the corresponding results in Duan (2017), Fan et al. (2018) [1,2] where a blow-up criterion in terms of the upper bounds of the density, the magnetic field and the temperature was obtained under the condition $2\mu \gt \lambda$. Our proof relies on some delicate energy estimates.

Citation

Download Citation

Xin Zhong. "Singularity Formation of the Non-barotropic Compressible Magnetohydrodynamic Equations Without Heat Conductivity." Taiwanese J. Math. 24 (3) 603 - 628, June, 2020. https://doi.org/10.11650/tjm/190701

Information

Received: 24 February 2019; Accepted: 30 June 2019; Published: June, 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07251189
MathSciNet: MR4100711
Digital Object Identifier: 10.11650/tjm/190701

Subjects:
Primary: 35B65, 76W05

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.24 • No. 3 • June, 2020
Back to Top