TY - JOUR
T1 - Existence and Decay of Global Strong Solution to 3D Density-Dependent Boussinesq Equations with Vacuum
AU - Gao , Cailong
AU - Ye , Xia
AU - Zhu , Mingxuan
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 360
EP - 370
PY - 2024
DA - 2024/06
SN - 6
DO - http://doi.org/10.12150/jnma.2024.360
UR - https://global-sci.org/intro/article_detail/jnma/23180.html
KW - Boussinesq equation, vacuum, global strong solution, exponential
decay-in-time.
AB - <p style="text-align: justify;">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 $[0, T].$</p>