Markov selections for the 3D stochastic Navier-Stokes equations

2006/02/27 by Franco Flandoli, Flandoli, F., Marco Romito +1 · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.math/0602612

Abstract

We investigate the Markov property and the continuity with respect to the initial conditions (strong Feller property) for the solutions to the Navier-Stokes equations forced by an additive noise. First, we prove, by means of an abstract selection principle, that there are Markov solutions to the Navier-Stokes equations. Due to the lack of continuity of solutions in the space of finite energy, the Markov property holds almost everywhere in time. Then, depending on the regularity of the noise, we prove that any Markov solution has the strong Feller property for regular initial conditions. We give also a few consequences of these facts, together with a new sufficient condition for well-posedness.

Cited by

• Compressible Euler equations with transport noise
• The Leibenson process

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