Random Perturbation of PDEs and Fluid Dynamic Models : École d'Été de Probabilités de Saint-Flour XL - 2010 / by Franco Flandoli.

Format:

Book

Author/Creator:

Flandoli, Franco, author.

Contributor:

SpringerLink (Online service)

Series:

École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 2015.

École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 2015

Language:

English

Subjects (All):

Distribution (Probability theory).

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (X, 182 pages 10 illustrations).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783642182310

Access Restriction:

Restricted for use by site license.