Random perturbation of PDEs and fluid dynamic models
Author(s)
Bibliographic Information
Random perturbation of PDEs and fluid dynamic models
（Lecture notes in mathematics, 2015 . École d'été de probabilités de Saint-Flour ; 40-2010）
Springer, c2011
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Random perturbation of PDEs and fluid dynamic models : École d'été de probabilités de Saint-Flour XL-2010
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2015200021319476
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Note
"40th Probability Summer School, Saint-Flour, France, July 4-17, 2010"--P. 171
Bibliography: p. 161-169
ISSN for subseries: 0721-5363
Description and Table of Contents
Description
The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.
Table of Contents
1. Introduction to Uniqueness and Blow-up.- 2. Regularization by Additive Noise.- 3. Dyadic Models.- 4. Transport Equation.- 5. Other Models. Uniqueness and Singularities
by "Nielsen BookData"