Existence and stability of dissipative turbulent solutions to a simple bi-fluid model of compressible fluids

TL;DR

This paper introduces and proves the existence of dissipative turbulent solutions for a bi-fluid compressible model, establishing their properties and uniqueness, thus expanding the understanding of generalized solutions in fluid dynamics.

Contribution

It defines a new class of dissipative turbulent solutions for a bi-fluid model and proves their existence, compatibility with classical solutions, and uniqueness properties.

Findings

Existence of dissipative turbulent solutions for all b3>1

Solutions are compatible with classical solutions

Weak-strong uniqueness principle holds for these solutions

Abstract

Following Abbatiello et al. [ DCCDS-A (41), 2020], we introduce dissipative turbulent solutions to a simple model of a mixture of two non interacting compressible fluids {\tc filling a bounded domain with general non zero inflow/outflow boundary conditions.} We prove existence of such solutions for all adiabatic coefficients $\gamma>1$, their compatibility with classical solutions, the relative energy inequality, and the weak strong uniqueness principle in this class. The class of dissipative turbulent solutions is so far the largest class of generalized solutions which still enjoys the weak strong uniqueness property.