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

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
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