TITLE:
Local Strong Solutions for the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum
AUTHORS:
Huifeng Wang
KEYWORDS:
Non-Homogeneous Incompressible Boussinesq Equation, Strong Solution, Vacuum, Cauchy Problem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.10,
October
22,
2019
ABSTRACT: The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.