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August 2020 Local strong solutions to the nonhomogeneous Bénard system with nonnegative density
Xin Zhong
Rocky Mountain J. Math. 50(4): 1497-1516 (August 2020). DOI: 10.1216/rmj.2020.50.1497

Abstract

We study the Cauchy problem of the nonhomogeneous Bénard system in the whole two-dimensional (2D) space, where the density is allowed to vanish initially. We prove that there exists a unique local strong solution. To compensate for the lack of integrability of the velocity in the whole space, a careful space weight is imposed on the initial density, which cannot decay too slowly in the far field.

Citation

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Xin Zhong. "Local strong solutions to the nonhomogeneous Bénard system with nonnegative density." Rocky Mountain J. Math. 50 (4) 1497 - 1516, August 2020. https://doi.org/10.1216/rmj.2020.50.1497

Information

Received: 18 October 2019; Accepted: 9 January 2020; Published: August 2020
First available in Project Euclid: 29 September 2020

zbMATH: 07261878
MathSciNet: MR4154821
Digital Object Identifier: 10.1216/rmj.2020.50.1497

Subjects:
Primary: 35Q35 , 76D03

Keywords: Cauchy problem , nonhomogeneous Bénard system , nonnegative density , strong solutions

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 4 • August 2020
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