Non-existence of classical solutions to a two-phase flow model with vacuum
arxiv(2024)
摘要
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.
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