Work

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

Year: 2025

Type: article

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.

Source: Nonlinearity

DOI: 10.1088/1361-6544/add231

Authors: Hai-Liang Li, Yuexun Wang, Yue Zhang

Institutions: Capital Normal University, Lanzhou University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Capital Normal University, National Natural Science Foundation of China

Awards: G1487269434, G2200368291, G2895501785