On new approach to the issue of existence and regularity for the steady compressible Navier--Stokes equations

Abstract

We prove existence of weak solutions to the steady compressible Navier--Stokes equations in isentropic regime. We consider the two-dimensional problem with the slip boundary conditions.

The proof is based on a new idea of the construction of approximative solutions which guarantees that the sought density belongs to the $L_\infty$ (up to the boundary). Our approach improves the known methods reducing number of technical tricks.

Keywords

• approach
• issue
• existence
• regularity
• steady
• compressible
• Navier--Stokes
• equations