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arXiv · 2402.02531

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

Hai-Liang Li·Yuexun Wang·Yue Zhang
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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.

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Hai-Liang Li, Yuexun Wang, Yue Zhang. 2024-02-04. Non-existence of classical solutions to a two-phase flow model with vacuum. https://doi.org/10.1088/1361-6544/add231

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