数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1293-1309.doi: 10.1007/s10473-022-0403-6

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GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION

晋雪婷1, 肖跃龙2, 于幻3   

  1. 1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Hunan, Xiangtan, 411105, China;
    3. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China
  • 收稿日期:2020-08-01 修回日期:2021-05-24 出版日期:2022-08-25 发布日期:2022-08-23
  • 通讯作者: Xueting Jin,E-mail:xuetingjin@163.com E-mail:xuetingjin@163.com
  • 基金资助:
    The research is partially supported by key research grant of the Academy for Multidisciplinary Studies, CNU. Yu is partially supported by NSFC (11901040) and Beijing Municipal Commission of Education (KM202011232020) and Beijing Natural Science Foundation (1204030).

GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION

Xueting Jin1, Yuelong Xiao2, Huan Yu3   

  1. 1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Hunan, Xiangtan, 411105, China;
    3. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China
  • Received:2020-08-01 Revised:2021-05-24 Online:2022-08-25 Published:2022-08-23
  • Contact: Xueting Jin,E-mail:xuetingjin@163.com E-mail:xuetingjin@163.com
  • Supported by:
    The research is partially supported by key research grant of the Academy for Multidisciplinary Studies, CNU. Yu is partially supported by NSFC (11901040) and Beijing Municipal Commission of Education (KM202011232020) and Beijing Natural Science Foundation (1204030).

摘要: In this paper, we prove the global well-posedness of the 2D Boussinesq equations with three kinds of partial dissipation; among these the initial data $(u_0,\theta_0)$ is required such that its own and the derivative of one of its directions $(x,y)$ are assumed to be $L^2(\mathbb R^2)$. Our results only need the lower regularity of the initial data, which ensures the uniqueness of the solutions.

关键词: Two-dimensional Boussinesq equations, global well-posedness, partial dissipation and diffusion

Abstract: In this paper, we prove the global well-posedness of the 2D Boussinesq equations with three kinds of partial dissipation; among these the initial data $(u_0,\theta_0)$ is required such that its own and the derivative of one of its directions $(x,y)$ are assumed to be $L^2(\mathbb R^2)$. Our results only need the lower regularity of the initial data, which ensures the uniqueness of the solutions.

Key words: Two-dimensional Boussinesq equations, global well-posedness, partial dissipation and diffusion

中图分类号: 

  • 35Q35