Asymptotic limit of the compressible Navier-Stokes system on domains with rough boundaries

TL;DR

This paper investigates the asymptotic behavior of solutions to the compressible Navier-Stokes equations on domains with oscillating boundaries, showing that the fluid adheres to the boundary in the limit under certain conditions.

Contribution

It provides a rigorous analysis of the fluid's asymptotic limit on rough domains with oscillating boundaries, extending understanding of boundary effects in compressible flows.

Findings

Fluid sticks to the boundary in the asymptotic limit

Boundary oscillations influence the limiting behavior

Results depend on non-degeneracy of boundary oscillations

Abstract

In this paper, we study the asymptotic behavior of solutions to the compressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the full-slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary, provided the oscillations are non-degenerate, meaning not oriented in a single direction.