Existence and Decay of Global Strong Solution to 3D Density-Dependent Boussinesq Equations with Vacuum
Year: 2024
Author: Cailong Gao, Xia Ye, Mingxuan Zhu
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 360–370
Abstract
This paper is concerned with the initial boundary problem for the three-dimensional density-dependent Boussinesq equations with vacuum. We obtain the existence of the global strong solution under the initial density in the norm $L^∞$ is small enough without any smallness condition of $u$ and $θ.$ Furthermore, the exponential decay rates of the solution and their derivatives in some norm was established. In addition, we show that the solution and their derivatives are monotonically decreasing with respect to time $t$ on $[0, T].$
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.360
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 360–370
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Boussinesq equation vacuum global strong solution exponential decay-in-time.