Burgers system driven by a periodic stochastic flow

Ya. G. Sinai
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Ya. G. Sinai: Princeton University, Department of Mathematics

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 347-353 from Springer

Abstract: 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 1 $$\frac{\partial u}{\partial t}+(u,\nabla )u=\mu \Delta u+\nabla \dot{B}(x,t)$$ or in the coordinate form 2 $$\frac{\partial {{u}_{i}}}{\partial t}+\sum\limits_{k=1}^{n}{\frac{\partial {{u}_{i}}}{\partial {{x}_{k}}}}\cdot {{u}_{k}}=\mu \Delta {{u}_{i}}+\frac{\partial }{\partial {{x}_{i}}}\dot{B}(x,t)$$ .

Keywords: Invariant Measure; Stochastic Differential Equation; Coordinate Form; Stochastic Partial Differential Equation; Wiener Measure (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68532-6_22

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DOI: 10.1007/978-4-431-68532-6_22

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