On the Regularity of Weak Solutions of the Boussinesq Equations in Besov Spaces

被引：12

作者：

Barbagallo, Annamaria ^{[1
]}

Gala, Sadek ^{[2
]}

Ragusa, Maria Alessandra ^{[3
,4
]}

Thera, Michel ^{[5
,6
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat R Caccioppoli, Via Cintia, I-80126 Naples, Italy

[2] Ecole Normale Super Mostaganem, Dept Sci Exactes, Box 227, Mostaganem 27000, Algeria

[3] Univ Catania, Dipartimento Matemat & Informat, Viale Andrea Doria 6, I-95125 Catania, Italy

[4] RUDN Univ, 6 Miklukho,Maklay St, Moscow 117198, Russia

[5] Univ Limoges, XLIM UMR CNRS 7252, Limoges, France

[6] Federat Univ Australia, Ctr Informat & Appl Optimisat, Ballarat, Vic, Australia

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2021年 / 49卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Boussinesq equations; Besov space; Weak solution; Regularity criterion; BLOW-UP CRITERION; SMOOTH SOLUTIONS; LOCAL EXISTENCE; SYSTEM; INEQUALITIES;

D O I：

10.1007/s10013-020-00420-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space (B) over dot(infinity,infinity)(-1), that, if the solution of the Boussinesq equation (1) below (starting with an initial data in H-2) is such that (del(u), del theta) is an element of L-2 (0, T; (B) over dot(infinity,infinity)(-1) (R-3)) then the solution remains smooth forever after T. In this contribution, we prove the same result for weak solutions just by assuming the condition on the velocity u and not on the temperature theta.

引用

页码：637 / 649

页数：13

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