Superdiffusivity of two dimensional lattice gas models

DOI10.1007/S10955-005-4297-1zbMATH Open1088.82016arXivmath/0505090OpenAlexW3100226680MaRDI QIDQ2574164

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Publication date: 18 November 2005

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Abstract: It was proved cite{EMYa, QY} 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 $loglogt$. Our argument indicates that the correct divergence rate is $(logt{)}^{1/2}$. This problem is closely related to the logarithmic correction of the time decay rate for the velocity auto-correlation function of a tagged particle.

Full work available at URL: https://arxiv.org/abs/math/0505090

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