Well-Posedness, Blow-up Criteria and Stability for Solutions of the Generalized MHD Equations in Sobolev-Gevrey Spaces

被引：6
|
作者：
Guterres, Robert H. [1 ]
Melo, Wilberclay G. [2 ]
Rocha, Nata F. [3 ]
Santos, Thyago S. R. [4 ]
机构：
[1] Univ Fed Pernambuco, Dept Matemat, BR-50670901 Recife, PE, Brazil
[2] Univ Fed Sergipe, Dept Matemat, BR-49100000 Sao Cristovao, SE, Brazil
[3] Univ Estadual Piaui, Campus Clovis Moura, BR-64078213 Teresina, PI, Brazil
[4] Inst Matematica Pura & Aplicada, IMPA, Estr Dona Catarina 110, BR-22460320 Rio De Janeiro, RJ, Brazil
来源：
ACTA APPLICANDAE MATHEMATICAE | 2021年 / 176卷 / 01期
关键词：
Generalized MHD equations; Existence of solutions; Blow-up criteria; Stability for global solutions; Sobolev-Gevrey spaces; LONG-TIME DECAY;
D O I：
10.1007/s10440-021-00448-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work presents the existence of local in time solutions for the generalized Magnetohydrodynamics equations in Sobolev-Gevrey (and Sobolev) spaces. Moreover, we establish the behavior of these solutions at potential blow-up times. In addition, if the initial data is assumed to be small enough, this paper proves the existence of global in time solutions, which are stable, in these same type of spaces.
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页数：30
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