arXiv subjects

Haiyan Yin

Publications and source records attributed to Haiyan Yin.

21 records · Page 2Linked to original sources

arXiv2015

Stability of contact discontinuity for the Navier-Stokes-Poisson system with free boundary

This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier-Stokes-Poisson system with free boundary in the case where the electron background density satisfies an analogue of the Boltzmann relation. We especially allow that the electric potential can take distinct constant states at boundary. On account of the quasineutral assumption, we first construct a viscous contact wave through the quasineutral Euler equations, and then prove that such a non-trivial profile is time-asymptotically stable under small perturbations for the corresponding initial boundary value problem of the Navier-Stokes-Poisson system. The analysis is based on the techniques developed in \cite{DL} and an elementary $L^2$ energy method.

math.AP↗

arXiv2015

Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier-Stokes-Poisson system

This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we successfully construct the boundary layer and rarefaction wave, and then we give the rigorous proofs of the stability theorems on the superposition of boundary layer and rarefaction wave under small perturbations for the corresponding initial boundary value problem of the Navier-Stokes-Poisson system, only provided the strength of boundary layer is small while the strength of rarefaction wave can be arbitrarily large. The complexity of nonlinear composite wave leads to many complicated terms in the course of establishing the {\it a priori} estimates. The proofs are given by an elementary $L^2$ energy method.

math.AP↗

arXiv2012

Global Classical Solutions of Viscous Liquid-gas Two-phase Flow Model

In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence of global classical solutions to the compressible Navier-Stokes equations was obtained by using the continuity methods under the assumption that the initial energy is sufficiently small.

math.AP↗