Random Perturbation of PDEs and Fluid Dynamic Models: ?cole d'?t? de Probabilit?s de Saint-Flour XL - 2010




Author: Franco Flandoli
Type: eBook
Date Released: 2011
Format: pdf
Language: English
Page Count: 192
Isbn10 Code: 3642182305
Isbn13 Code: 9783642182310


From the Back Cover This volume 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.

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