Large time decay for the magnetohydrodynamics equations in Sobolev-Gevrey spaces

被引：6
|
作者：
Guterres, Robert [1 ]
Melo, Wilberclay G. [2 ]
Nunes, Juliana [3 ]
Perusato, Cilon [4 ]
机构：
[1] Univ Fed Rio Grande do Sul, Dept Matemat Pura & Aplicada, BR-91509900 Porto Alegre, RS, Brazil
[2] Univ Fed Sergipe, Dept Matemat, BR-49100000 Sao Cristovao, SE, Brazil
[3] Univ Fed Rio Grande, Inst Matemat Estat & Fis, BR-96203900 Rio Grande, RS, Brazil
[4] Univ Fed Pernambuco, Dept Matemat, BR-50670901 Recife, PE, Brazil
来源：
MONATSHEFTE FUR MATHEMATIK | 2020年 / 192卷 / 03期
关键词：
Magnetohydrodynamics equations; Sobolev-Gevrey spaces; Large time decay; BLOW-UP CRITERION; FLUID;
D O I：
10.1007/s00605-020-01415-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Our paper shows that global solutions (u,b)is an element of C([0,infinity); H-alpha,sigma(s)(R3)), of the Magnetohydrodynamics equations present the following asymptotic behavior: lim(t ->infinity) t(s/2) parallel to (u, b)(t)parallel to(2)((H)) (over dota,sigma (R3)) = 0, where a > 0, sigma > 1, s > 1/2 and s not equal 3/2. It is important to point out that the assumption related to existence of global solutions for this same system can be made since the existence and uniqueness of local solutions were recently established; more precisely, it has been proved that there is a time T>0 such that (u,b)is an element of C([0,T]; H-a,sigma(s)(R-3)).
引用
收藏
页码：591 / 613
页数：23
相关论文
共 50 条
  • [1] Large time decay for the magnetohydrodynamics equations in Sobolev–Gevrey spaces
    Robert Guterres
    Wilberclay G. Melo
    Juliana Nunes
    Cilon Perusato
    Monatshefte für Mathematik, 2020, 192 : 591 - 613
  • [2] 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
  • [3] Local existence, uniqueness and lower bounds of solutions for the magnetohydrodynamics equations in Sobolev-Gevrey spaces
    Melo, Wilberclay G.
    Rocha, Nata Firmino
    Zingano, Paulo R.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 482 (01)
  • [4] LONG TIME DECAY FOR 3D NAVIER-STOKES EQUATIONS IN SOBOLEV-GEVREY SPACES
    Benameur, Jamel
    Jlali, Lotfi
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [5] Asymptotic behavior of solutions for the 2D micropolar equations in Sobolev-Gevrey spaces
    Melo, Wilberclay G.
    Rocha, Nata F.
    Zingano, Paulo R.
    ASYMPTOTIC ANALYSIS, 2021, 123 (1-2) : 157 - 179
  • [6] Generalized Weinstein Sobolev-Gevrey spaces and pseudo-differential operators
    Ben Mohamed, Hassen
    Chaffar, Mohamed Moktar
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (01) : 273 - 292
  • [7] Decay Rates for Mild Solutions of the Quasi-Geostrophic Equation with Critical Fractional Dissipation in Sobolev-Gevrey Spaces
    Wilberclay G. Melo
    Natã Firmino Rocha
    Natielle dos Santos Costa
    Acta Applicandae Mathematicae, 2023, 186
  • [8] Decay Rates for Mild Solutions of the Quasi-Geostrophic Equation with Critical Fractional Dissipation in Sobolev-Gevrey Spaces
    Melo, Wilberclay G.
    Rocha, Nata Firmino
    dos Santos Costa, Natielle
    ACTA APPLICANDAE MATHEMATICAE, 2023, 186 (01)
  • [9] Existence of solutions and their behavior for the anisotropic quasi-geostrophic equation in Sobolev and Sobolev-Gevrey spaces
    Melo, Wilberclay G.
    Santos, Thyago S. R.
    Costa, Natielle dos Santos
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (01)
  • [10] 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
12345