Hyperbolic Scaling Limits: The Method of Compensated Compactness

J. Fritz

2010, v.16, №1, 117-138

ABSTRACT

Hydrodynamic limit of various models with hyperbolic (Euler) scaling law is discussed, we are mainly interested in the limiting behavior of the microscopic systems in a regime of shocks. In the absence of an effective coupling anadvanced method of PDE theory: compensated compactness is required. We consider some deterministic and Ginzburg - Landau models of classical statistical mechanics; the proof of several recent results is outlined. Microscopic systems living on the infinite line are preferred.

Keywords: interacting exclusions,hyperbolic scaling,Lax entropy pairs,compensated compactness,logarithmic Sobolev inequalities,relaxation schemes

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