Burgers system driven by a periodic stochastic flow

  • Ya. G. Sinai


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
$$\frac{\partial u}{\partial t}+(u,\nabla )u=\mu \Delta u+\nabla \dot{B}(x,t)$$
or in the coordinate form
$$\frac{\partial {{u}_{i}}}{\partial t}+\sum\limits_{k=1}^{n}{\frac{\partial {{u}_{i}}}{\partial {{x}_{k}}}}\cdot {{u}_{k}}=\mu \Delta {{u}_{i}}+\frac{\partial }{\partial {{x}_{i}}}\dot{B}(x,t)$$


Invariant Measure Stochastic Differential Equation Coordinate Form Stochastic Partial Differential Equation Wiener Measure 
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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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