Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation

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Abstract

As a continuation of the previous work [48], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The argument is based on the nonlinear lower bounds for the fractional Laplacian established in [13]. Consequently, this result significantly improves the recent works [13], [45], [48].

MSC

35Q35
35B65
76D03

Keywords

2D Boussinesq equations
Fractional Laplacian dissipation
Global regularity

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