Remarks on the improved regularity criterion for the 2D Euler–Boussinesq equations with supercritical dissipation

被引:0
作者
Zhuan Ye
机构
[1] Jiangsu Normal University,Department of Mathematics and Statistics
来源
Zeitschrift für angewandte Mathematik und Physik | 2016年 / 67卷
关键词
2D Boussinesq equations; Supercritical dissipation; Regularity criterion; Besov space; 35Q35; 35B65; 76D03;
D O I
暂无
中图分类号
学科分类号
摘要
This paper is devoted to the investigation of the regularity criterion to the two-dimensional (2D) Euler–Boussinesq equations with supercritical dissipation. By making use of the Littlewood–Paley technique, we provide an improved regularity criterion involving the temperature at the scaling invariant level, which improves the previous results.
引用
收藏
相关论文
共 65 条
[1]  
Adhikari D(2016)Global regularity results for the 2D Boussinesq equations with partial dissipation J. Differ. Equ. 260 1893-1917
[2]  
Cao C(2013)Global regularity for the 2D anisotropic Boussinesq equations with vertical dissipation Arch. Ration. Mech. 208 985-1004
[3]  
Shang H(2006)Global regularity for the 2D Boussinesq equations with partial viscosity terms Adv. Math. 203 497-513
[4]  
Wu J(1997)Local existence and blow-up criterion for the Boussinesq equations Proc. R. Soc. Edinb. Sect. A 127 935-946
[5]  
Xu X(1999)Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations Nagoya Math. J. 155 55-80
[6]  
Ye Z(2007)A new Bernstein inequality and the 2D dissipative quasigeostrophic equation Commun. Math. Phys. 271 821-838
[7]  
Cao C(2012)Nonlinear maximum principles for dissipative linear nonlocal operators and applications Geom. Funct. Anal. 22 1289-1321
[8]  
Wu J(2008)Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation Ann. Inst. H. Poincare Anal. Non Lineaire 25 1103-1110
[9]  
Chae D(2009)Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations Ann. Inst. H. Poincare Anal. Non Lineaire 26 159-180
[10]  
Chae D(2012)Local well-posedness and blow up criterion for the inviscid Boussinesq system in Hölder spaces J. Partial Differ. Equ. 25 220-238