Global regularity results for the 2D Boussinesq equations with vertical dissipation |
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Authors: | Dhanapati Adhikari Chongsheng Cao |
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Institution: | a Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, USA b Department of Mathematics, Florida International University, Miami, FL 33199, USA |
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Abstract: | This paper furthers the study of Adhikari et al. (2010) 2] on the global regularity issue concerning the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. It is shown here that the vertical velocity v of any classical solution in the Lebesgue space Lq with 2?q<∞ is bounded by C1q for C1 independent of q. This bound significantly improves the previous exponential bound. In addition, we prove that, if v satisfies , then the associated solution of the 2D Boussinesq equations preserve its smoothness on 0,T]. In particular, implies global regularity. |
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Keywords: | 35A05 35B45 35B65 76D03 76D09 |
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