scholarly journals Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain

2022 ◽  
Vol 38 (1) ◽  
pp. 1-27
Author(s):  
Yanjin Wang & Zhouping Xin
Keyword(s):  
Well Posedness ◽  
Strip Domain

Global well-posedness for the 2D MHD equations without magnetic diffusion in a strip domain

Nonlinearity ◽  
2016 ◽  
Vol 29 (4) ◽  
pp. 1257-1291 ◽  
Author(s):  
Xiaoxia Ren ◽  
Zhaoyin Xiang ◽  
Zhifei Zhang
Keyword(s):  
Mhd Equations ◽  
Well Posedness ◽  
Magnetic Diffusion ◽  
Strip Domain

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

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