数学物理学报(英文版) ›› 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

叶专   

  1. School of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
  • 收稿日期:2014-01-10 修回日期:2014-05-16 出版日期:2015-01-20 发布日期:2015-01-20
  • 基金资助:

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

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.

摘要:

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 .

关键词: Boussinesq equations, fractional Laplacian, global regularity

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

中图分类号: 

  • 35Q35