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Caricature of hydrodynamics for lattice dynamics

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Caricature of hydrodynamics for lattice dynamics

Content Provider	Springer Nature Link
Author	Dudnikova, T. V.
Copyright Year	2012
Abstract	We consider the lattice dynamics in the half-space, with zero boundary condition. The initial data are supposed to be random function. We introduce the family of initial measures {µ 0 ɛ , ɛ > 0} depending on a small scaling parameter ɛ. We assume that the measures µ 0 ɛ are locally homogeneous for space translations of order much less than ɛ $^{−1}$ and nonhomogeneous for translations of order ɛ $^{−1}$. Moreover, the covariance of µ 0 ɛ decreases with distance uniformly in ɛ. Given τ ∈ ℝ / 0, r ∈ ℝ + d , and κ > 0, we consider the distributions of random solution in the time moments t = τ/ɛ $_{ κ }$ and at lattice points close to [r/ɛ] ∈ ℤ + d . Themain goal is to study the asymptotic behavior of these distributions as ɛ → 0 and to derive the limit hydrodynamic equations of the Euler or Navier-Stokes type.
Starting Page	245
Ending Page	258
Page Count	14
File Format	PDF
ISSN	20700466
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume Number	4
Issue Number	4
e-ISSN	20700474
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2012-11-05
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	harmonic crystals in the half-space mixing problem random initial data covariance matrices weak convergence of measures Gaussian measures hydrodynamic limit hydrodynamic space-time scaling Euler and Navier-Stokes equations Algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Deriving hydrodynamic equations for lattice systems

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