Probability & incompressible Navier-Stokes equations: An overview of some recent developments
| Autor: | Edward C. Waymire |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Statistics and Probability
Class (set theory) multi-type branching random walk incompressible Navier-Stokes multiplicative cascade 60H30 35Q30 60J80 76D05 (Primary) mild solution FOS: Mathematics Applied mathematics Navier–Stokes equations Probabilistic framework Mathematics 60J80 Partial differential equation Probability (math.PR) Probabilistic logic 76D05 Orientation (vector space) stochastic iteration 35Q30 Fourier transform background radiation process majorizing kernels Compressibility 60H30 Focus (optics) Mathematics - Probability |
| Zdroj: | Probab. Surveys 2 (2005), 1-32 |
| ISSN: | 1549-5787 |
| DOI: | 10.1214/154957805100000078 |
| Popis: | 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. Comment: Published at http://dx.doi.org/10.1214/154957805100000078 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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