Zero-relaxation-time limits in the hydrodynamic equations for plasmas revisited. (English) Zbl 0963.35115

Jüngel, Ansgar; Peng, Yue-Jun

Z. Angew. Math. Phys. 51, No. 3, 385-396 (2000).

This paper gives a rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations governing a plasma. The equations comprise the Euler equations for electrons and/or ions coupled with a linear or nonlinear Poisson equation. The proof, that relies on certain high energy estimates for the Euler equations, makes use of compactness arguments. It is shown that the result obtained in the form of a key theorem is valid for all adiabatic states for both electrons and ions. Attention is also drawn to the fact that the uniqueness question for solutions of the degenerate drift-diffusion equations is only partially solved.

Reviewer: A.Jeffrey (Newcastle upon Tyne)

MSC:

35L60	First-order nonlinear hyperbolic equations
82D10	Statistical mechanical studies of plasmas
35B40	Asymptotic behavior of solutions to PDEs
35Q35	PDEs in connection with fluid mechanics

Keywords:

compensated compactness; high energy estimates for the Euler equations