The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian

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Abstract

As a microscopic model we consider a system of interacting continuum like spin field over Rd. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.

Original languageEnglish
Pages (from-to)519-562
Number of pages44
JournalProbability Theory and Related Fields
Volume90
Issue number4
DOIs
Publication statusPublished - 1991 Dec
Externally publishedYes

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Hydrodynamic Limit
Ginzburg-Landau
Hydrodynamics
Interaction
Nonlinear Diffusion Equation
Homogenization
Continuum
Space-time
Scaling
Converge
Model

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "As a microscopic model we consider a system of interacting continuum like spin field over Rd. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.",
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