Hydrodynamic Limits

Hydrodynamic Limits and Related Topics

This book is an account of a mini–course called Lectures on Hydrodynamic Scaling by S.R.S. Varadhan, followed by a workshop on “Hydrodynamic Limits”, both held in October 1998, at the Fields Institute for Research in Mathematical Sciences in Toronto, Canada. In this report, we mainly focus on Part I of the book, containing the notes by S.R.S. Varadhan. Part II is devoted to papers by the speake...

The two-scale approach to hydrodynamic limits for non-reversible dynamics

In [2], a new method to study hydrodynamic limits, called the two-scale approach, was developed for reversible dynamics. In this work, we generalize this method to a family of nonreversible dynamics. As an application, we obtain quantitative rates of convergence to the hydrodynamic limit for a weakly asymmetric version of the Ginzburg-Landau model endowed with Kawasaki dynamics. These results a...

The Energy Transport and the Drift Di usionEquations as Relaxation Limits of theHydrodynamic Model

Two relaxation limits of the hydrodynamic model for semiconductors are investigated. Using the compensated compactness tools we show the convergence of (scaled) entropy solutions of the hydrodynamic model to the solutions of the energy transport and the drift{diiusion equations, according respectively to diierent time scales.

N ov 2 00 8 Semiclassical and relaxation limits of bipolar quantum hydrodynamic model ∗

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R. We prove that the unique strong solution converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and to that of the classical Drift-Diffusion system under the combined relaxation an...

Zero–Relaxation–Time Limits in the Hydrodynamic Equations for Plasmas Revisited

A rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations for plasmas is given. The equations consist of the Euler equations for the electrons and/or ions coupled with a linear or nonlinear Poisson equation. The proof is based on high energy estimates for the Euler equations and appropriate compactness arguments. The theorem is valid for all adiabatic states for both ele...

Zero-Mass-Electrons Limits in Hydrodynamic Models for Plasmas