Random Perturbation of PDEs and Fluid Dynamic Models
École d'Été de Probabilités de Saint-Flour XL - 2010
Published on 2. March 2011
X, 182 pages
978-3-642-18231-0 (ISBN)
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.
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Franco Flandoli
Random Perturbation of PDEs and Fluid Dynamic Models
École d'Été de Probabilités de Saint-Flour XL - 2010
Book
03/2011
1st Edition
Springer
€37.40
Shipment within 7-9 days
Content
1. Introduction to Uniqueness and Blow-up.- 2. Regularization by Additive Noise.- 3. Dyadic Models.- 4. Transport Equation.- 5. Other Models. Uniqueness and Singularities
