Global strong solutions of the MHD system with zero resistivity in a bounded domain

2018 ◽  
Vol 291 (17-18) ◽  
pp. 2557-2564
Author(s):  
Jishan Fan ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Strong Solutions ◽  
Global Strong Solutions ◽  
Mhd System

scholarly journals GLOBAL STRONG SOLUTIONS OF THE DENSITY-DEPENDENT INCOMPRESSIBLE MHD SYSTEM WITH ZERO RESISTIVITY IN A BOUNDED DOMAIN

2019 ◽  
Vol 24 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Jishan Fan ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Initial Density ◽  
Strong Solutions ◽  
Regularity Criterion ◽  
Well Posedness ◽  
Density Dependent ◽  
Bootstrap Argument ◽  
Global Strong Solutions ◽  
Mhd System ◽  
Incompressible Mhd

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with . We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.

scholarly journals Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Representation Formula ◽  
Critical Space ◽  
Lebesgue Spaces ◽  
Initial Value ◽  
Dirac Equations ◽  
Nonlinear Dirac Equations ◽  
Global Strong Solutions ◽  
Solution Representation

We study the initial value problem of some nonlinear Dirac equations which areLmℝcritical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solutionU∈L∞0,T; Ym+2ℝ.

Sign in / Sign up

Export Citation Format

Share Document