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arXiv · 1506.00470

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

Zhuan Ye·Xiaojing Xu
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Abstract

As a continuation of the previous work [40], 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 [12]. Consequently, this result significantly improves the recent works [12, 38, 40].

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Zhuan Ye, Xiaojing Xu. 2015-06-01. Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation. https://doi.org/10.1007/s00021-015-0245-2

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