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Superdiffusivity of Two Dimensional Lattice Gas Models

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Abstract

It was proved [Navier–Stokes Equations for Stochastic Particle System on the Lattice. Comm. Math. Phys. (1996) 182, 395; Lattice gases, large deviations, and the incompressible Navier–Stokes equations. Ann. Math. (1998) 148, 51] that stochastic lattice gas dynamics converge to the Navier–Stokes equations in dimension d=3 in the incompressible limits. In particular, the viscosity is finite. We proved that, on the other hand, the viscosity for a two dimensional lattice gas model diverges faster than (log t)1/2. Our argument indicates that the correct divergence rate is (log t)1/2. This problem is closely related to the logarithmic correction of the time decay rate for the velocity auto-correlation function of a tagged particle.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina, 110, CEP 22460, Rio de Janeiro, Brasil

    Claudio Landim

  2. CNRS UMR 6085, Université de Rouen, 76128, Mont Saint Aignan, France

    Claudio Landim

  3. Escuela de Matemáticas, Universidad de Costa Rica, San José, 2060, Costa Rica

    José A. Ramírez

  4. Department of Mathematics, Stanford University, CA, 94305, USA

    Horng-Tzer Yau

Authors
  1. Claudio Landim
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  2. José A. Ramírez
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  3. Horng-Tzer Yau
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Correspondence to Horng-Tzer Yau.

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Landim, C., Ramírez, J.A. & Yau, HT. Superdiffusivity of Two Dimensional Lattice Gas Models. J Stat Phys 119, 963–995 (2005). https://doi.org/10.1007/s10955-005-4297-1

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  • DOI: https://doi.org/10.1007/s10955-005-4297-1

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