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

共 50 条

[1] Well-Posedness, Blow-up Criteria and Stability for Solutions of the Generalized MHD Equations in Sobolev-Gevrey Spaces
Robert H. Guterres
Wilberclay G. Melo
Natã F. Rocha
Thyago S. R. Santos
Acta Applicandae Mathematicae, 2021, 176
[2] Navier-Stokes equations: local existence, uniqueness and blow-up of solutions in Sobolev-Gevrey spaces
Melo, Wilberclay G.
Rocha, Nata Firmino
Barbosa, Ezequiel
APPLICABLE ANALYSIS, 2021, 100 (09) : 1905 - 1924
[3] Well-posedness and blow-up criterion for strong solutions of a class of compressible MHD equations
Meng, Qiu
Xing, Huifang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 539 (02)
[4] On the Blow-up Criterion of 3D-NSE in Sobolev-Gevrey Spaces
Benameur, Jamel
Jlali, Lotfi
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2016, 18 (04) : 805 - 822
[5] Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations
Jeong, Eunji
Kim, Junha
Lee, Jihoon
ADVANCES IN MATHEMATICAL PHYSICS, 2018, 2018
[6] Time decay rates for the generalized MHD-α equations in Sobolev-Gevrey spaces
Melo, Wilberclay G.
Rosa Santos, Thyago Souza
APPLICABLE ANALYSIS, 2022, 101 (18) : 6623 - 6644
[7] Local well-posedness and blow-up criteria of solutions for a rod equation
Zhou, Y
MATHEMATISCHE NACHRICHTEN, 2005, 278 (14) : 1726 - 1739
[8] Existence, uniqueness and blow-up of solutions for the 3D Navier-Stokes equations in homogeneous Sobolev-Gevrey spaces
Braze e Silva, P.
Melo, W. G.
Rocha, N. F.
COMPUTATIONAL & APPLIED MATHEMATICS, 2020, 39 (02):
[9] On well-posedness of the Cauchy problem for 3D MHD system in critical Sobolev-Gevrey space
Chaabani, Abdelkerim
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2021, 2 (02):
[10] New blow-up criteria for local solutions of the 3D generalized MHD equations in Lei-Lin-Gevrey spaces
Melo, Wilberclay G. G.
Rocha, Nata Firmino
MATHEMATISCHE NACHRICHTEN, 2023, 296 (02) : 757 - 778

← 1 2 3 4 5 →