TITLE:
Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum
AUTHORS:
Min Liu
KEYWORDS:
Non-Homogeneous Incompressible Boussinesq Equation, Strong Solution, Large Time Behavior, Existence and Uniqueness
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.10,
October
15,
2019
ABSTRACT: We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case.