Global Existence and Uniqueness of Pathwise Solution to the Stochastic 2D Inviscid Boussinesq Equations

Abstract

Global well-posedness of 2D inviscid Boussinesq equations is unsolved. In the present work, we find that if this inviscid hydrodynamics equation is perturbed by noise, the global well-posedness holds in high probability with initial data satisfies a certain Gevrey-type bound. Moreover, the unique global solution to the stochastic inviscid 2D Boussinesq equation is bounded by the initial data.

Keywords

Stochastic Boussinesq equations / Regularity / Gevrey spaces / Mathematical Sciences / Statistics

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Funding

National Natural Science Foundation of China(11971077)

Fundamental Research Funds for Central Universities(2020CDJ-LHZZ-027)

Key Laboratory of Nonlinear Analysis and its Applications (Chongqing University), Ministry of Education(Chongqing University)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature