A Blow-Up Criterion for the Density-Dependent Incompressible Magnetohydrodynamic System with Zero Viscosity

Author:

Shi Kunlong1,Fan Jishan2,Nakamura Gen3

Affiliation:

1. College of Sciences, Nanjing Forestry University, Nanjing 210037, China

2. Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China

3. Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Abstract

In this paper, we provide a blow-up criterion for the density-dependent incompressible magnetohydrodynamic system with zero viscosity. The proof uses the Lp-method and the Kato–Ponce inequalities in the harmonic analysis. The novelty of our work lies in the fact that we deal with the case in which the resistivity η is positive.

Funder

National Natural Science Foundation of China

Publisher

MDPI AG

Reference12 articles.

1. On the Euler equations for the nonhomogeneous fluids II;Valli;J. Math. Anal. Appl.,1980

2. Existence of C∞ solutions of the Euler equations for nonhomogeneous fluids;Valli;Commun. Partial Differ. Equ.,1980

3. About the motion of nonhomogeneous ideal incompressible fluids;Valli;Nonlinear Anal. TMA,1988

4. Berselli, L. (1995). On the Global Existence of Solution to the Equation of Ideal Fluids. [Master’s Thesis]. (In Italian).

5. On the well-posedness of the incompressible density-dependent Euler equations in the Lp framework;Danchin;J. Differ. Equ.,2010

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3