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

Edward C. Waymire, Oregon State University

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 (1997) and extended by Bhattacharya et al (2003, 2004). 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.

AMS 2000 subject classifications: Primary 60H30, 35Q30; secondary 60J80, 76D05.

Keywords: incompressible Navier-Stokes, Fourier transform, mild solution, multi-type branching random walk, multiplicative cascade, background radiation process, majorizing kernels, stochastic iteration.

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Waymire, Edward C., Probability & incompressible Navier-Stokes equations: An overview of some recent developments, Probability Surveys, 2, (2005), 1-32 (electronic).


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