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

S. Albeverio; Ya. Belopolskaya

doi:10.4067/S0719-06462010000200006

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

S. Albeverio albeverio@uni-bonn.de
Ya. Belopolskaya yana@yb1569.spb.edu

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DOI:

https://doi.org/10.4067/S0719-06462010000200006

Abstract

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.

Keywords

Stochastic flows , diffusion processes , nonlinear parabolic equations , Cauchy problem

S. Albeverio Institut f¨ur Angewandte Mathematik, Universit¨at Bonn, Wegelerstr. 6, D-53115 Bonn, Germany. SFB 611, HCM, Bonn, BiBoS, Bielefeld - Bonn, CERFIM, Locarno and USI (Switzerland).
Ya. Belopolskaya St.Petersburg State University for Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, 190005, St.Petersburg, Russia.

Pages: 77–96
Date Published: 2010-06-01
Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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Published

2010-06-01

How to Cite

[1]

S. Albeverio and Y. Belopolskaya, “Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes”, CUBO, vol. 12, no. 2, pp. 77–96, Jun. 2010.