Initial boundary value problem for 2D Boussinesq equations with temperature-dependent diffusion

Huapeng Li, Ronghua Pan, Weizhe Zhang
2015 Journal of Hyperbolic Differential Equations  
We consider the initial-boundary value problem of two-dimensional inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the initial-boundary value problem for H 3 initial data. Moreover, we will show that the temperature converges exponentially to zero as time
more » ... to infinity, and the velocity and vorticity are uniformly bounded in time.
doi:10.1142/s0219891615500137 fatcat:kjs6ds6swjaajhm5jikv6xhqtm