Non-existence of classical solutions to a two-phase flow model with vacuum

Abstract

In this paper, we study the well-posedness of classical solutions to a two-phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier-Stokes equations via a drag forcing term. We consider the case that the fluid densities may contain a vacuum, and the viscosities are density-dependent functions. Under suitable assumptions on the initial data, we show that the finite-energy (i.e., in the inhomogeneous Sobolev space) classical solutions to the Cauchy problem of this coupled system do not exist for any small time.

References in corpus (6)

• Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity
• Well-posedness for a multi-dimensional viscous liquid-gas two-phase flow model
• Non-Existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier-Stokes Equations
• Weak solutions for some compressible multicomponent fluid models
• Finite-energy solutions for compressible two-fluid Stokes system
• Global existence of weak solutions to the drift-flux system for general pressure laws