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.

引用

页数：30

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