Random Perturbation of PDEs and Fluid Dynamic Models

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.

List 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

Product details

• Authors: Franco Flandoli
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2011
• EAN: 9783642182303
• ISBN: 978-3-642-18230-3
• No. of pages: 182
• Dimensions: 155 mm x 236 mm x 13 mm
• Weight: 311 g
• Illustrations: X, 182 p. 10 illus.
• Series: Lecture Notes in Mathematics; École d'Été de Probabilités de Saint-Flour
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Stochastik, B, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory