Two phase flows of compressible viscous fluids

TL;DR

This paper introduces a new variational concept of dissipative varifold solutions for two-phase compressible viscous fluids, providing an alternative to Young measure-based approaches and establishing existence results for complex fluid models.

Contribution

The paper develops a novel variational framework for modeling two-phase compressible viscous fluids, extending the mathematical theory beyond existing Young measure methods.

Findings

Existence of dissipative varifold solutions for a broad class of viscous fluids.

The new formulation combines energy and momentum inequalities into a single variational principle.

Applicable to fluids with non-linear viscous stress dependence.

Abstract

We introduce a new concept of dissipative varifold solution to models of two phase compressible viscous fluids. In contrast with the existing approach based on the Young measure description, the new formulation is variational combining the energy and momentum balance in a single inequality. We show the existence of dissipative varifold solutions for a large class of general viscous fluids with non--linear dependence of the viscous stress on the symmetric velocity gradient.