Probability & incompressible Navier-Stokes equations: An overview of some recent developments

Details Probability & incompressible Navier-Stokes equations: An overview of some recent developments Probability & incompressible Navier-Stokes equations: An overview of some recent developments

2005-11-10

arxiv.org/abs/math/0511266v1

Probability Surveys 2005, Vol. 2, 1-32

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957805100000078 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957805100000078

This is largely an attempt to provide probabilists some orientation to an important class of non-linear partial differential equations in applied mathematics, the incompressible Navier-Stokes equations. Particular focus is given to the probabilistic framework introduced by LeJan and Sznitman [Probab. Theory Related Fields 109 (1997) 343-366] and extended by Bhattacharya et al. [Trans. Amer. Math. Soc. 355 (2003) 5003-5040; IMA Vol. Math. Appl., vol. 140, 2004, in press]. In particular this is an effort to provide some foundational facts about these equations and an overview of some recent results with an indication of some new directions for probabilistic consideration.

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