Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (1): 112-120.doi: 10.1016/S0252-9602(14)60144-2

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A NOTE ON GLOBAL WELL-POSEDNESS OF SOLUTIONS TO BOUSSINESQ EQUATIONS WITH FRACTIONAL DISSIPATION

YE Zhuan   

  1. School of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
  • Received:2014-01-10 Revised:2014-05-16 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    The author was partially supported by NSFC (11171026; 11371059), BNSF (2112023) and the Fundamental Research Funds for the Central Universities of China.

Abstract:

The goal of this paper is to consider the global well-posedness to n-dimensional (n  3) Boussinesq equations with fractional dissipation. More precisely, it is proved that there exists a unique global regular solution to the Boussinesq equations provided the real parameter satisfies  1 2 + n 4 .

Key words: Boussinesq equations, fractional Laplacian, global regularity

CLC Number: 

  • 35Q35
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