scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

scholarly journals On the well-posedness and large-time behavior of higher order Boussinesq system

Nonlinearity ◽  
2019 ◽  
Vol 32 (5) ◽  
pp. 1852-1881 ◽  
Author(s):  
Roberto A Capistrano-Filho ◽  
Fernando A Gallego ◽  
Ademir F Pazoto
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Higher Order ◽  
Boussinesq System ◽  
Well Posedness ◽  
Time Behavior

scholarly journals Large Time Behavior of Solutions to the Nonlinear Heat Equation with Absorption with Highly Singular Antisymmetric Initial Values

2020 ◽  
Vol 20 (2) ◽  
pp. 311-337
Author(s):  
Hattab Mouajria ◽  
Slim Tayachi ◽  
Fred B. Weissler
Keyword(s):  
Heat Equation ◽  
Large Time ◽  
Large Time Behavior ◽  
Nonlinear Heat Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Well Posedness ◽  
Time Behavior ◽  
Initial Values ◽  
Self Similar ◽  
Similar Solutions

AbstractIn this paper, we study global well-posedness and long-time asymptotic behavior of solutions to the nonlinear heat equation with absorption, {u_{t}-\Delta u+\lvert u\rvert^{\alpha}u=0}, where {u=u(t,x)\in\mathbb{R}}, {(t,x)\in(0,\infty)\times\mathbb{R}^{N}} and {\alpha>0}. We focus particularly on highly singular initial values which are antisymmetric with respect to the variables {x_{1},x_{2},\ldots,x_{m}} for some {m\in\{1,2,\ldots,N\}}, such as {u_{0}=(-1)^{m}\partial_{1}\partial_{2}\cdots\partial_{m}\lvert\,{\cdot}\,% \rvert^{-\gamma}\in\mathcal{S}^{\prime}(\mathbb{R}^{N})}, {0<\gamma<N}. In fact, we show global well-posedness for initial data bounded in an appropriate sense by {u_{0}} for any {\alpha>0}. Our approach is to study well-posedness and large time behavior on sectorial domains of the form {\Omega_{m}=\{x\in\mathbb{R}^{N}:x_{1},\ldots,x_{m}>0\}}, and then to extend the results by reflection to solutions on {\mathbb{R}^{N}} which are antisymmetric. We show that the large time behavior depends on the relationship between α and {\frac{2}{\gamma+m}}, and we consider all three cases, α equal to, greater than, and less than {\frac{2}{\gamma+m}}. Our results include, among others, new examples of self-similar and asymptotically self-similar solutions.

scholarly journals Large time behavior for the full compressible magnetohydrodynamic flows

2012 ◽  
Vol 11 (3) ◽  
pp. 959-971
Author(s):  
Geonho Lee ◽  
◽  
Sangdong Kim ◽  
Young-Sam Kwon ◽  
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows
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