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2005 Probability & incompressible Navier-Stokes equations: An overview of some recent developments
Edward C. Waymire
Probab. Surveys 2: 1-32 (2005). DOI: 10.1214/154957805100000078

Abstract

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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Edward C. Waymire. "Probability & incompressible Navier-Stokes equations: An overview of some recent developments." Probab. Surveys 2 1 - 32, 2005. https://doi.org/10.1214/154957805100000078

Information

Published: 2005
First available in Project Euclid: 28 February 2005

zbMATH: 1189.76424
MathSciNet: MR2121794
Digital Object Identifier: 10.1214/154957805100000078

Subjects:
Primary: 35Q30 , 60H30 , 60J80 , 76D05

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

Rights: Copyright © 2005 The Institute of Mathematical Statistics and the Bernoulli Society

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