Blow-up criterion for the density dependent inviscid Boussinesq equations

被引：0
作者：
Li Li
Yanping Zhou
机构：
[1] China Three Gorges University,College of Science
[2] China Three Gorges University,College of Science & Three Gorges Mathematical Research Center
来源：
Boundary Value Problems | / 2020卷
关键词：
Inviscid Boussinesq equations; Density-dependent; Local existence; Blow-up criterion; 35Q35; 76B03;
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摘要：
In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in RN(N≥2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{N}\ (N\geq 2)$\end{document}. By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.
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