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STABILITY OF THE 3D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION NEAR THE HYDROSTATIC BALANCE
  • Youhua Wei,
  • LIYA JIANG,
  • KAIGE YANG
Youhua Wei
Chengdu University of Technology

Corresponding Author:[email protected]

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LIYA JIANG
Chengdu University of Technology
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KAIGE YANG
Chengdu University of Technology
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Abstract

The Boussinesq equations with partial or fractional dissipation not only naturally generalize the classical Boussinesq equations, but also are physically relevant and mathematically important. Unfortunately, it is not often well understood for many ranges of fractional powers. This paper focuses on a system of the 3D Boussinesq equations with fractional horizontal ( − ∆ h ) α u and ( − ∆ h ) β θ dissipation and proves that if an initial data ( u 0 , θ 0 ) in the Sobolev space H 3 ( R 3 ) close enough to the hydrostatic balance state, respectively, the equations with α , β ∈ ( 1 2 , 1 ] then always lead to a steady solution.
02 Nov 2022Submitted to Mathematical Methods in the Applied Sciences
03 Nov 2022Submission Checks Completed
03 Nov 2022Assigned to Editor
08 Nov 2022Review(s) Completed, Editorial Evaluation Pending
13 Nov 2022Reviewer(s) Assigned
13 Jan 2023Editorial Decision: Revise Minor
16 Jan 20231st Revision Received
25 Feb 2023Assigned to Editor
25 Feb 2023Submission Checks Completed
25 Feb 2023Review(s) Completed, Editorial Evaluation Pending
28 Feb 2023Reviewer(s) Assigned
07 Mar 2023Editorial Decision: Revise Minor
11 Mar 20232nd Revision Received
12 Mar 2023Submission Checks Completed
12 Mar 2023Assigned to Editor
12 Mar 2023Review(s) Completed, Editorial Evaluation Pending
14 Mar 2023Reviewer(s) Assigned
14 Mar 2023Editorial Decision: Accept