Existence and Decay of Global Strong Solution to 3D Density-Dependent Boussinesq Equations with Vacuum (Journal of Nonlinear Modeling and Analysis, 2024)
This paper is concerned with the initial boundary problem for thethree-dimensional density-dependent Boussinesq equations with vacuum. Weobtain the existence of the global strong solution under the initial density inthe norm $L^∞$ is small enough without any smallness condition of $u$ and $θ.$ Furthermore, the exponential decay rates of the solution and their derivativesin some norm was established. In addition, we show that the solution andtheir derivatives are monotonically decreasing with respect to time $t$ on $[0, T].$
Keywords: Boussinesq equation; vacuum; global strong solution; exponential decay-in-time.