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Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes

2010; University of La Frontera; Volume: 12; Issue: 2 Linguagem: Espanhol

10.4067/s0719-06462010000200006

0719-0646

Sergio Albeverio, Ya. I. Belopolskaya,

Stability and Controllability of Differential Equations

We reduce the construction of a weak solution of the Cauchy problem for the Navier-Stokes system to the construction of a stochastic problem solution.Under suitable conditions we solve the stochastic problem and prove that simultaneously we obtain a weak (generalized) solution to the Cauchy problem for the Navier-Stokes system. RESUMENNosotros reducimos la construcción de una solución débil de un problema de Cauchy para el sistema de Navier-Stokes para la construcción de la resolución de un problema estocástico.Bajo condiciones convenientes resolvimos el problema estocástico y probamos que simultáneamente obtenemos una solución débil (generalizada) para el problema de Cauchy del sistema de Navier-Stokes.