Generalized dissipative solutions to free boundary compressible viscous models

TL;DR

This paper introduces generalized dissipative solutions for free boundary compressible viscous fluid models, encompassing non-Newtonian behaviors and bridging free flow and congested regions, with proofs of existence and conditions for classical solutions.

Contribution

It establishes the existence of generalized dissipative solutions for complex free boundary compressible viscous models, including nonlinear viscosities and non-Newtonian fluids.

Findings

Existence of generalized dissipative solutions proven.

Smooth solutions are shown to be classical solutions.

Applicable to models with nonlinear viscosities and free boundaries.

Abstract

We study free boundary compressible viscous models that may include nonlinear viscosities. These are compressible/incompressible Navier-Stokes type systems for a non-Newtonian stress tensor. They describe the motion of a possibly non-Newtonian fluid in free flow and in congested regions. In the congested regions it appears the pressure that is the Lagrange multiplier associated with the incompressibility constraint, while in free flows it is a pressureless gas system. We establish the existence of generalized dissipative solutions in the case of in/out-flow boundary conditions and we also prove that if these solutions are smooth then they are classical solutions.