English

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

Analysis of PDEs 2025-05-12 v1

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.

Keywords

Cite

@article{arxiv.2402.02531,
  title  = {Non-existence of classical solutions to a two-phase flow model with vacuum},
  author = {Hai-Liang Li and Yuexun Wang and Yue Zhang},
  journal= {arXiv preprint arXiv:2402.02531},
  year   = {2025}
}