Global Regularity Results of the 2D Boussinesq Equations with Fractional Laplacian Dissipation |
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| Authors: | Zhuan Ye Xiaojing Xu |
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| Affiliation: | 1.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education,Beijing Normal University,Beijing,People’s Republic of China |
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| Abstract: | In this paper, we study the 2D Boussinesq equations with fractional Laplacian dissipation. In particular, we prove the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The main ingredient of the proof is the utilization of the Hölder estimates for advection fractional-diffusion equations as well as Littlewood–Paley technique. |
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