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Burgers system driven by a periodic stochastic flow

  • Ya. G. Sinai

Abstract

Burgers System (BS) is Navier-Stokes system without pressure and incompressibility. It is one of the most popular models of hydrodynamics and has a lot of applications. In this paper, we consider BS driven by a potential force whose potential is a periodic stochastic flow. If x = (x 1,... x n) is the vector of coordinates and u = (u 1,..., u„) is the velocity vector then the n-dimensional BS takes the form
$$\frac{\partial u}{\partial t}+(u,\nabla )u=\mu \Delta u+\nabla \dot{B}(x,t)$$
(1)
or in the coordinate form
$$\frac{\partial {{u}_{i}}}{\partial t}+\sum\limits_{k=1}^{n}{\frac{\partial {{u}_{i}}}{\partial {{x}_{k}}}}\cdot {{u}_{k}}=\mu \Delta {{u}_{i}}+\frac{\partial }{\partial {{x}_{i}}}\dot{B}(x,t)$$
(2)
.

Keywords

Invariant Measure Stochastic Differential Equation Coordinate Form Stochastic Partial Differential Equation Wiener Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • Ya. G. Sinai
    • 1
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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