Blow-Up Criterion for the 3D Non-resistive Compressible Magnetohydrodynamic Equations

被引：2

作者：

Xi, Shuai ^{[1
,2
]}

Zhu, Shengguo ^{[2
,3
,4
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[4] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2020年 / 32卷 / 02期

基金：

澳大利亚研究理事会; 上海市自然科学基金; 中国国家自然科学基金;

关键词：

MHD; Strong solutions; Vacuum; Compatibility condition; Blow-up criterion; NAVIER-STOKES EQUATIONS; CLASSICAL-SOLUTIONS; GLOBAL-SOLUTIONS; LARGE OSCILLATIONS; SMOOTH SOLUTIONS; REGULARITY; BOUNDARY;

D O I：

10.1007/s10884-019-09756-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove a blow-up criterion in terms of the magnetic field H and the mass density rho for the strong solutions to the initial boundary value problem of the 3D isentropic compressible MHD equations with zero magnetic diffusion and initial vacuum. More precisely, we show that the upper bounds of (H,rho) control the possible blow-up (see Rozanova in Proceedings of symposia in applied mathematics, 2009; Xin in Commun Pure Appl Math 51:0229-0240, 1998; Yuan and Zhao in Kinet Relat Models 7:195-203, 2014) for strong solutions.

引用

页码：769 / 790

页数：22

共 50 条

[31] LOCAL EXISTENCE AND BLOW-UP CRITERION OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS
Kim, Jae-Myoung
[J]. ACTA MATHEMATICA SCIENTIA, 2018, 38 (06) : 1759 - 1766
[32] On the blow-up criterion of smooth solutions to the 3D ideal MHD equations
Zhang Z.-F.
Liu X.-F.
[J]. Acta Mathematicae Applicatae Sinica, 2004, 20 (4) : 695 - 700
[33] Energy conservation of the resistive and the non-resistive magnetohydrodynamic equations
Chen, Qionglei
Zhang, Qi
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (04) : 1994 - 2005
[34] EXISTENCE AND A BLOW-UP CRITERION OF SOLUTION TO THE 3D COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS WITH FINITE ENERGY
Suen, Anthony
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (03) : 1775 - 1798
[35] A Note on the Blow-up Criterion of Smooth Solutions to the 3D Incompressible MHD Equations
Sadek GALA
[J]. Acta Mathematicae Applicatae Sinica, 2012, (04) : 639 - 642
[36] Osgood type blow-up criterion for the 3D Boussinesq equations with partial viscosity
Shang, Zhaoyang
[J]. AIMS MATHEMATICS, 2018, 3 (01): : 1 - 11
[37] A note on the blow-up criterion of smooth solutions to the 3D incompressible MHD equations
Gala, Sadek
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2012, 28 (04): : 639 - 642
[38] A note on the blow-up criterion of smooth solutions to the 3D incompressible MHD equations
Sadek Gala
[J]. Acta Mathematicae Applicatae Sinica, English Series, 2012, 28 : 639 - 642
[39] Existence Results and Blow-Up Criterion of Compressible Radiation Hydrodynamic Equations
Li, Yachun
Zhu, Shengguo
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2017, 29 (02) : 549 - 595
[40] Existence Results and Blow-Up Criterion of Compressible Radiation Hydrodynamic Equations
Yachun Li
Shengguo Zhu
[J]. Journal of Dynamics and Differential Equations, 2017, 29 : 549 - 595

← 1 2 3 4 5 →