Year: 2022
Author: Feng Cheng
Communications in Mathematical Research , Vol. 38 (2022), Iss. 4 : pp. 579–604
Abstract
In this paper, we study the zero viscosity-diffusivity limit for the incompressible Boussinesq equations in a periodic domain in the framework of Gevrey class. We first prove that there exists an interval of time, independent of the viscosity coefficient and the diffusivity coefficient, for the solutions to the viscous incompressible Boussinesq equations. Then, based on these uniform estimates, we show that the solutions of the viscous incompressible Boussinesq equations converge to that of the ideal incompressible Boussinesq equations as the viscosity and diffusivity coefficients go to zero. Moreover, the convergence rate is also given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0075
Communications in Mathematical Research , Vol. 38 (2022), Iss. 4 : pp. 579–604
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Gevrey class incompressible Boussinesq equation analyticity zero viscosity-diffusivity limit convergence rate.