LARGE-TIME REGULAR SOLUTIONS TO THE MODIFIED QUASI-GEOSTROPHIC EQUATION IN BESOV SPACES

被引：4
|
作者：
Tan, Wen [1 ]
Dong, Bo-Qing [1 ]
Chen, Zhi-Min [1 ]
机构：
[1] Shenzhen Univ, Sch Math & Stat, Shenzhen 518052, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Modified quasi-geostrophic equations; Besov spaces; local well-posedness; smoothing effect; large-time global regular solutions; GLOBAL WELL-POSEDNESS; NAVIER-STOKES EQUATIONS; MAXIMUM-PRINCIPLES; INITIAL DATA; CRITERION;
D O I：
10.3934/dcds.2019152
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the study of the modified quasi-geostrophic equation partial derivative(t)theta + u . del theta + nu Lambda(alpha)theta = 0 with u = Lambda R-beta(perpendicular to)theta in R-2. By the Littlewood-Paley theory, we obtain the local well-posedness and the smoothing effect of the equation in critical Besov spaces. These results are applied to show the global existence of regular solutions for the critical case beta = alpha - 1 and the existence of regular solutions for large time t > T with respect to the supercritical case beta > alpha - 1 in Besov spaces. Earlier results for the equation in Hilbert spaces H-s spaces are improved.
引用
收藏
页码：3749 / 3765
页数：17
相关论文
共 50 条
  • [41] The Surface Quasi-geostrophic Equation With Random Diffusion
    Buckmaster, Tristan
    Nahmod, Andrea
    Staffilani, Gigliola
    Widmayer, Klaus
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020, 2020 (23) : 9370 - 9385
  • [42] On the regularity criteria of a surface quasi-geostrophic equation
    Yamazaki, Kazuo
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 4950 - 4956
  • [43] Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation
    Yamamoto, Masakazu
    Sugiyama, Yuusuke
    NONLINEARITY, 2019, 32 (07) : 2467 - 2480
  • [44] Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior
    Iwabuchi, Tsukasa
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (03): : 687 - 713
  • [45] On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation
    Ye, Zhuan
    NONLINEARITY, 2020, 33 (01) : 72 - 105
  • [46] Global well-posedness for a modified critical dissipative quasi-geostrophic equation
    Miao, Changxing
    Xue, Liutang
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (01) : 792 - 818
  • [47] Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces
    Azanzal, Achraf
    Allalou, Chakir
    Melliani, Said
    Abbassi, Adil
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2023, 36 (01): : 1 - 21
  • [48] Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing
    Cannone, Marco
    Miao, Changxing
    Xue, Liutang
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2013, 106 : 650 - 674
  • [49] Commutator estimate and its application to regularity criteria of the dissipative quasi-geostrophic equation
    Chen, Jianwen
    Chen, Zhi-Min
    Dong, Bo-Qing
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 329 : 84 - 91
  • [50] On the well-posedness of the quasi-geostrophic equation in the Triebel-Lizorkin-Lorentz spaces
    Zhaoyin Xiang
    Wei Yan
    Journal of Evolution Equations, 2011, 11 : 241 - 263
12345