Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions

Abstract

<p style="text-indent:20px;">We are concerned with the large-time asymptotic behaviors towards the planar rarefaction wave to the three-dimensional (3D) compressible and isentropic Navier-Stokes equations in half space with Navier boundary conditions. It is proved that the planar rarefaction wave is time-asymptotically stable for the 3D initial-boundary value problem of the compressible Navier-Stokes equations in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^+\times \mathbb{T}^2 $\end{document}</tex-math></inline-formula> with arbitrarily large wave strength. Compared with the previous work [<xref ref-type="bibr" rid="b17">17</xref>, <xref ref-type="bibr" rid="b16">16</xref>] for the whole space problem, Navier boundary conditions, which state that the impermeable wall condition holds for the normal velocity and the fluid tangential velocity is proportional to the tangential component of the viscous stress tensor on the boundary, are crucially used for the stability analysis of the 3D initial-boundary value problem.</p>