Remarks on pressure blow-up criterion of the 3D zero-diffusion Boussinesq equations in margin Besov spaces
type: Item
instance of: scholarly article
title: Remarks on pressure blow-up criterion of the 3D zero-diffusion Boussinesq equations in margin Besov spaces
zbMATH Open document ID: 1404.35352
DOI: 10.1155/2017/6754780
author: Min Fu
author: Chao Cai
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: This study is focused on the pressure blow-up criterion for a smooth solution of three-dimensional zero-diffusion Boussinesq equations. With the aid of Littlewood-Paley decomposition together with the energy methods, it is proved that if the pressure satisfies the following condition on margin Besov spaces, \(\pi(x, t) \in L^{2 /(2 + r)}(0, T; \dot{B}_{\infty,\infty}^r)\) for \(r = \pm 1,\) then the smooth solution can be continually extended to the interval \((0, T^\ast)\) for some \(T^\ast > T\). The findings extend largely the previous results.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 6962654
zbMATH Keywords: blow-up criterion
zbMATH Keywords: smooth solution
zbMATH Keywords: Boussinesq equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6754780
OpenAlex ID: W2608793689
Wikidata QID: Q59142458
cites work: Q4798343
cites work: Q3199050
cites work: Q3593809
cites work: Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation
cites work: The regularity of weak solutions of the 3D Navier-Stokes equations in \(B^{-1}_{\infty,\infty}\)
cites work: On the weak-strong uniqueness of Koch-Tataru's solution for the Navier-Stokes equations
cites work: Structure of the set of stationary solutions of the navier‐stokes equations
cites work: Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain
cites work: Blow-up criteria for 3D Boussinesq equations in the multiplier space
cites work: Blow-up criterion of smooth solutions for the Boussinesq equations
cites work: REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS
cites work: A note on regularity criterion for the 3D Boussinesq system with partial viscosity
cites work: Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion
cites work: Q5247814
cites work: 三维部分粘性Boussinesq 方程的爆破准则
cites work: An improved regularity criterion of three-dimensional magnetohydrodynamic equations
cites work: On the regularity criteria of the 3D Navier-Stokes equations in critical spaces
cites work: On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations
cites work: Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices
cites work: A remark on the regularity criterion of Boussinesq equations with zero heat conductivity
cites work: Remarks on the logarithmical regularity criterion of the supercritical surface quasi-geostrophic equation in Morrey spaces
cites work: Asymptotic convergence rate of supercritical surface quasi-geostrophic equation in Morrey space
cites work: Q4782579
cites work: Q4210480
cites work: Oscillating Patterns in Some Nonlinear Evolution Equations
cites work: Commutator estimates and the euler and navier-stokes equations
description: scientific article; zbMATH DE number 6962654