Global existence of mild solutions for 3D stochastic Boussinesq system in Besov spaces

Jinyi Sun, Ning Li and Minghua Yang

Mathematische Nachrichten, 2025, vol. 298, issue 4, 1105-1126

Abstract: The paper is concerned with the three‐dimensional stochastic Boussinesq system driven by an additive white noise, describing the motion of viscous incompressible fluids with density stratification phenomenon in the rotational framework. By striking new balances between the smoothing effects of the Laplacian dissipation and dispersion effects caused by the Coriolis force and density stratification, we prove existence and uniqueness of global mild solutions to the three‐dimensional stochastic Boussinesq system for arbitrarily large initial data and stochastic external forces in Besov spaces, provided that the stratification parameter is large enough. Our results can be regarded as a generalization of [Math. Nachr. 290(2017), 613–631] and [Indiana Univ. Math. J. 66(2017), 2037–2070].

Date: 2025
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