Yachun Li

From two-fluid Euler–Poisson equations to one-fluid Euler equations

We consider quasi-neutral limits in two-fluid isentropic Euler-Poisson equations arising in the modeling of unmagnetized plasmas and semiconductors. For periodic smooth solutions, we justify an asymptotic expansion in a time interval independent of the Debye length. This implies the convergence of the equations to compressible Euler equations. The proof is based on energy estimates for symmetrizable hyperbolic equations and on the exploration of the coupling between the Euler equations and the Poisson equation.

Non-relativistic limits of rarefaction wave to the 1-D piston problem for the isentropic relativistic Euler equations

We consider the 1-D piston problem for the isentropic relativistic Euler equations when the total variations of the initial data and the speed of the piston are both sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we study the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic isentropic Euler equations as the light speed c→+∞.

A Boundary Value Problem for a Class of Anisotropic Degenerate Parabolic–Hyperbolic Equations

We consider a mixed type boundary value problem for a class of degenerate parabolic–hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary condition; in the other, we impose a Neumann condition. We apply a normal trace formula for L2-divergence-measure fields to prove a new strong trace property in the part of the boundary where the Neumann condition is imposed. We prove the existence and uniqueness of the entropy solution.