Markov selections for the 3D stochastic Navier-Stokes equations

Details Markov selections for the 3D stochastic Navier-Stokes equations Markov selections for the 3D stochastic Navier-Stokes equations

2006-02-27

arxiv.org/abs/math/0602612v2

Mathematics

Probability

59 pages; corrected several errors and typos, added references

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Markov selections for the 3D stochastic Navier-Stokes equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Markov selections for the 3D stochastic Navier-Stokes equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Markov selections for the 3D stochastic Navier-Stokes equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-485872