A probabilistic approach to the two-dimensional Navier-Stokes equations (Q1577736)
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scientific article; zbMATH DE number 1496106
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A probabilistic approach to the two-dimensional Navier-Stokes equations |
scientific article; zbMATH DE number 1496106 |
Statements
A probabilistic approach to the two-dimensional Navier-Stokes equations (English)
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30 June 2002
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Probabilistic representation of solutions of Navier-Stokes equations, represented in terms of the vorticity, leads to a system of equations, where the first one looks like a Feynman-Kac formula \(\xi(t,x)=E[\xi_0(X(t,x))]\) but the equation for \(X\) includes \(\xi\). The paper shows that for an initial vorticity in \(L^p\cap L^q\), \(1\leq p<2<q\), there exists a unique solution, and the method of proof is constructive.
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Navier-Stokes equations
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stochastic differential equations
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