Steady compressible Oseen flow with slip boundary conditions

TL;DR

This paper proves the existence of solutions for a steady compressible Oseen flow with slip boundary conditions in a convex 2D domain, using regularization and Helmholtz decomposition techniques.

Contribution

It introduces a new method combining regularization and Helmholtz decomposition to establish solution existence under specific boundary geometry conditions.

Findings

Existence of solutions in H^2 x H^1 space for the system.

Solution construction via regularization of weak solutions.

Applicability under certain boundary geometry assumptions.

Abstract

We prove the existence of solution in a class H^2(\Omega) x H^1(\Omega) to steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with the boundary of class H^{5/2}. The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to a problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under additional assumption on the geometry of the boundary.