Markov selections for the 3D stochastic Navier–Stokes equations

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 Nav...

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Bibliographic Details
Published in:	Probability theory and related fields Vol. 140; no. 3-4; pp. 407 - 458
Main Authors:	Flandoli, Franco, Romito, Marco
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-03-2008 Springer Springer Nature B.V
Subjects:	Boundary conditions Continuity Economics Energy Exact sciences and technology Finance Fluid flow General topics Initial conditions Insurance Linear equations Management Markov analysis Mathematical analysis Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Navier-Stokes equations Noise Operations Research/Decision Theory Parametric inference Probability Probability and statistics Probability Theory and Stochastic Processes Quantitative Finance Sciences and techniques of general use Statistics Statistics for Business Stochastic analysis Studies Theoretical Three dimensional imaging Markov selections 76M35 Markov property Strong Feller property Well posedness 60H30 Stochastic Navier–Stokes equations 76D05 35Q30 60H15 Martingale problem Additive noise Initial condition Well posedness, 76D05 Probability theory Feller property Sufficient condition Navier Stokes equation Stochastic Navier-Stokes equations Stochastic equation
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