Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces

Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces

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...

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Main Authors: Min Fu, Chao Cai
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2017/6754780
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spelling doaj-5db1b5d802a5451caeb207110cd408942021-07-02T02:25:09ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/67547806754780Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov SpacesMin Fu0Chao Cai1State Key Laboratory for Multispectral Information Processing Technologies, School of Automation, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory for Multispectral Information Processing Technologies, School of Automation, Huazhong University of Science and Technology, Wuhan, ChinaThis 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, π(x,t)∈L2/(2+r)(0,T;B˙∞,∞r) for r=±1, then the smooth solution can be continually extended to the interval (0,T⁎) for some T⁎>T. The findings extend largely the previous results.http://dx.doi.org/10.1155/2017/6754780
collection DOAJ
language English
format Article
sources DOAJ
author Min Fu
Chao Cai
spellingShingle Min Fu
Chao Cai
Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
Advances in Mathematical Physics
author_facet Min Fu
Chao Cai
author_sort Min Fu
title Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
title_short Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
title_full Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
title_fullStr Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
title_full_unstemmed Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces
title_sort remarks on pressure blow-up criterion of the 3d zero-diffusion boussinesq equations in margin besov spaces
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2017-01-01
description 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, π(x,t)∈L2/(2+r)(0,T;B˙∞,∞r) for r=±1, then the smooth solution can be continually extended to the interval (0,T⁎) for some T⁎>T. The findings extend largely the previous results.
url http://dx.doi.org/10.1155/2017/6754780
work_keys_str_mv AT minfu remarksonpressureblowupcriterionofthe3dzerodiffusionboussinesqequationsinmarginbesovspaces
AT chaocai remarksonpressureblowupcriterionofthe3dzerodiffusionboussinesqequationsinmarginbesovspaces
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