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Elementary symmetrization of inviscid two-fluid flow equations giving a number of instant results. (arXiv:1810.04386v1 [math.AP])
来源于:arXiv
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 liqui 查看全文>>