Global solutions to three-dimensional generalized MHD equations with large initial data

2019 ◽  
Vol 70 (3) ◽  
Author(s):  
Fagui Liu ◽  
Yu-Zhu Wang
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Global Solutions ◽  
Mhd Equations ◽  
Large Initial Data ◽  
Generalized Mhd Equations

Global solutions to a hyperbolic-parabolic coupled system with large initial data

2009 ◽  
Vol 29 (3) ◽  
pp. 629-641 ◽  
Author(s):  
Guo Jun ◽  
Xiao Jixiong ◽  
Zhao Huijiang ◽  
Zhu Changjiang
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Coupled System ◽  
Large Initial Data

scholarly journals Global well-posedness for the three-dimensional incompressible viscous non-resistive MHD equations in an infinite slab

2021 ◽  
Author(s):  
Youyi Zhao
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Well Posedness ◽  
Lagrangian Coordinates ◽  
Mathematical Approach ◽  
Compatibility Conditions ◽  
Finite Height ◽  
Infinite Slab ◽  
Mhd System

In this paper, we investigate the global well-posedness of the system of incompressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no nonlinear compatibility conditions on the initial data.

Finite time blow-up of complex solutions of the conserved Kuramoto–Sivashinsky equation in ℝd and in the torus 𝕋d, d ⩾ 1

2019 ◽  
Vol 149 (5) ◽  
pp. 1175-1188
Author(s):  
Léo Agélas
Keyword(s):  
Sobolev Space ◽  
Initial Data ◽  
Besov Space ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Large Initial Data ◽  
Complex Solutions ◽  
Complex Valued ◽  
Sivashinsky Equation

AbstractWe consider complex-valued solutions of the conserved Kuramoto–Sivashinsky equation which describes the coarsening of an unstable solid surface that conserves mass and that is parity symmetric. This equation arises in different aspects of surface growth. Up to now, the problem of existence and smoothness of global solutions of such equations remained open in ℝd and in the torus 𝕋d, d ⩾ 1. In this paper, we answer partially to this question. We prove the finite time blow-up of complex-valued solutions associated with a class of large initial data. More precisely, we show that there is complex-valued initial data that exists in every Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the complex-valued solution is in no Besov space (and hence in no Lebesgue or Sobolev space).

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