Linglong Du, Haitao Wang
Published 2017-06-19Version 1
In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound speed in two opposite directions and reflected heat kernel (due to the boundary effect) propagating with positive sound speed. With the strong wave interactions, the nonlinear analysis exhibits the rich wave structure: the diffusion waves interact with each other and consequently, the solution decays with algebraic rate.
Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
On Davies' conjecture and strong ratio limit properties for the heat kernel
On elliptic equations in a half space or in convex wedges with irregular coefficients
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