Global well-posedness for 2D Boussinesq system with general supercritical dissipation
type: Item
instance of: scholarly article
title: Global well-posedness for 2D Boussinesq system with general supercritical dissipation
zbMATH Open document ID: 1338.35359
author: Daoyuan Fang
author: Chenyin Qian
author: Ting Zhang
published in: Nonlinear Analysis. Real World Applications
publication date: 2015-12-22T00:00:00Z
review text: The authors consider a Cauchy problem of the 2D incompressible generalized Boussinesq equations with the fractional Laplacian dissipation, for the velocity vector field, the pressure and the temperature. This system is associated to the Zygmund operator and to other operator defined by the Fourier transform. The Boussinesq system is a model to describe the geophysical flows, such as oceanic circulation and atmospheric fronts and is similar to the 2D incompressible Navier-Stokes system. In the supercritical case, the authors established the local well-posedness results for the Boussinesq system with suitable initial data and gave two blow-up criteria in terms of velocity and temperature. The main aim of this paper is to obtain a blow-up criteria better than previous and to prove the global well-posedness result with the small initial data. The results are obtained by using the Fourier localization method.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35S30
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 6523605
zbMATH Keywords: 2D Boussinesq equations
zbMATH Keywords: well-posedness
zbMATH Keywords: blow-up criterion
zbMATH Keywords: supercritical dissipation
zbMATH Keywords: Fourier localization method
reviewed by: Marin I. Marin
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2015.08.004
OpenAlex ID: W1416720419
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DOI: 10.1016/J.NONRWA.2015.08.004
description: scientific article; zbMATH DE number 6523605