Affiliation:
1. College of Mathematics and Physics, Geomathematics Key Laboratory of Sichuan Province Chengdu University of Technology 610059 Chengdu China
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
and
dissipation and proves that if the initial data (
) in the Sobolev space
are close enough to the hydrostatic balance state, respectively, the equations with
then always lead to a steady solution.
Funder
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics
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