TY - JOUR

T1 - Elementary symmetrization of inviscid two-fluid flow equations giving a number of instant results

AU - Ruan, Lizhi

AU - Trakhinin, Yuri

N1 - Publisher Copyright: © 2018 Elsevier B.V.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid–gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and particles. Introducing an entropy-like function, we reduce the equations of both models to a symmetric form which looks like the compressible Euler equations written in the nonconservative form in terms of the pressure, the velocity and the entropy. Basing on existing results for the Euler equations, this gives a number of instant results for both models. In particular, we conclude that all compressive shock waves in these models exist locally in time. For the 2D case, we make the conclusion about the local-in-time existence of vortex sheets under a “supersonic” stability condition. In the sense of a much lower regularity requirement for the initial data, our result for 2D vortex sheets essentially improves a recent result for vortex sheets in the liquid–gas two-phase flow.

AB - We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid–gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and particles. Introducing an entropy-like function, we reduce the equations of both models to a symmetric form which looks like the compressible Euler equations written in the nonconservative form in terms of the pressure, the velocity and the entropy. Basing on existing results for the Euler equations, this gives a number of instant results for both models. In particular, we conclude that all compressive shock waves in these models exist locally in time. For the 2D case, we make the conclusion about the local-in-time existence of vortex sheets under a “supersonic” stability condition. In the sense of a much lower regularity requirement for the initial data, our result for 2D vortex sheets essentially improves a recent result for vortex sheets in the liquid–gas two-phase flow.

KW - COMPRESSIBLE VORTEX SHEETS

KW - GLOBAL WEAK SOLUTIONS

KW - BLOW-UP CRITERION

KW - 2-PHASE FLOW

KW - ASYMPTOTIC ANALYSIS

KW - STOKES SYSTEM

KW - MODEL

KW - STABILITY

KW - EXISTENCE

KW - BEHAVIOR

UR - http://www.scopus.com/inward/record.url?scp=85058950155&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2018.11.008

DO - 10.1016/j.physd.2018.11.008

M3 - Article

AN - SCOPUS:85058950155

VL - 391

SP - 66

EP - 71

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -