Publication at Faculty of Mathematics and Physics |
2023
Abstract
We study a mathematical model of a viscous compressible fluid obeying the slip boundary condition of friction type. We present a notion of weak solutions to this model, in which the momentum equation and the associated energy inequality are combined into a single relation.
Moreover, the slip boundary condition of friction type is incorporated into this relation by the use of a boundary integral. Our main result proves the existence of such weak solutions.
The proof of this result combines the classical existence theory for the compressible Navier-Stokes equations with an approximation of the aforementioned boundary integral via a convex regularization of the absolute value function.