BEALE-KATO-MAJDA TYPE CRITERION OF SMOOTH SOLUTIONS FOR THE THREE DIMENSIONAL BOUSSINESQ EQUATIONS VIA PARTIAL HORIZONTAL DERIVATIVES OF TWO VELOCITY COMPONENTS

被引：0

作者：

Ben Omrane, Ines ^{[1
]}

机构：

[1] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 90950, Riyadh 11623, Saudi Arabia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2025年 / 18卷 / 02期

关键词：

Boussinesq equations; blow-up criterion; Sobolev and Besov spaces; smooth solution; variational and interpolation inequalities; BLOW-UP CRITERION; IMPROVED REGULARITY CRITERION; LOCAL EXISTENCE; BESOV-SPACES;

D O I：

10.3934/dcdss.2024015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a blow-up criterion for the local smooth solutions to the three-dimensional incompressible Boussinesq equations in the framework of Besov spaces B0 infinity,infinity via partial horizontal derivatives of two velocity components partial differential 1u1 and partial differential 2u2. Our result can be regarded as the borderline case of the work by F. Wu (Bull. Braz. Math. Soc., New Series (52) 2021, 267-279).

引用

页码：350 / 358

页数：9

共 26 条

[1] A REGULARITY CRITERION TO THE 3D BOUSSINESQ EQUATIONS
Alghamdi, A. M.
Ben Omrane, I
Gala, S.
Ragusa, M. A.
[J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 1795 - 1804
[2] A regularity criterion of weak solutions to the 3D Boussinesq equations
Alghamdi, Ahmad Mohammed
Gala, Sadek
Ragusa, Maria Alessandra
[J]. AIMS MATHEMATICS, 2017, 2 (03): : 451 - U208
[3] CANNON JR, 1980, LECT NOTES MATH, V771, P129
[4] Local existence and blow-up criterion of Holder continuous solutions of the Boussinesq equations
Chae, D
Kim, SK
Nam, HS
[J]. NAGOYA MATHEMATICAL JOURNAL, 1999, 155 : 55 - 80
[5] Local existence and blow-up criterion for the Boussinesq equations
Chae, D
Nam, HS
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 : 935 - 946
[6] Infinite Prandtl number convection
Constantin, P
Doering, CR
[J]. JOURNAL OF STATISTICAL PHYSICS, 1999, 94 (1-2) : 159 - 172
[7] Dong BQ, 2011, ACTA MATH SCI, V31, P591
[8] A note on regularity criterion for the 3D Boussinesq system with partial viscosity
Fan, Jishan
Zhou, Yong
[J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (05) : 802 - 805
[9] Regularity criteria for the 3D density-dependent Boussinesq equations
Fan, Jishan
Ozawa, Tohru
[J]. NONLINEARITY, 2009, 22 (03) : 553 - 568
[10] Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices
Gala, Sadek
Ragusa, Maria Alessandra
[J]. APPLICABLE ANALYSIS, 2016, 95 (06) : 1271 - 1279

← 1 2 3 →