On the Hydrodynamic Limit of a Scalar Ginzburg-Landau Lattice Model: The Resolvent Approach

  • J. Fritz
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 9)

Abstract

A d-dimensional lattice system of continuous spins is considered, the evolution law is given by an infinite system of locally coupled stochastic differential equations. In view of the construction of the model, the evolution is reversible in time, and the mean spin satisfies a conservation law, thus we have a whole family of equilibrium Gibbs states parametrized by the associated chemical potential. The asymptotic behaviour of the system is investigated in the framework of hydrodynamic (Navier-Stokes) scaling. The initial, local equilibrium distribution is specified by letting the chemical potential of the equilibrium state be inhomogeneous in space. We show that the macroscopic fluctuations vanish in the hydrodynamic limit, and the limiting profile of the mean spin satisfies a nonlinear diffusion equation. Some very recent results and the main ideas of the proofs are summarized.

Keywords

Entropy 

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • J. Fritz
    • 1
  1. 1.Mathematical Institute HASBudapestHungary

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