GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION

doi:10.1007/s10473-022-0403-6

Abstract

Abstract: In this paper, we prove the global well-posedness of the 2D Boussinesq equations with three kinds of partial dissipation; among these the initial data $(u_0,\theta_0)$ is required such that its own and the derivative of one of its directions $(x,y)$ are assumed to be $L^2(\mathbb R^2)$. Our results only need the lower regularity of the initial data, which ensures the uniqueness of the solutions.

Key words: Two-dimensional Boussinesq equations, global well-posedness, partial dissipation and diffusion

CLC Number:

35Q35

Xueting Jin, Yuelong Xiao, Huan Yu. GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION[J].Acta mathematica scientia,Series B, 2022, 42(4): 1293-1309.

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