Random Perturbation of PDEs and Fluid Dynamic Models: École d’Été de Probabilités de Saint-Flour XL – 2010: 2015 (Lecture Notes in Mathematics, 2015) - Softcover

Flandoli, Franco

Softcover

ISBN 10: 3642182305 ISBN 13: 9783642182303

Publisher: Springer, 2011

Synopsis

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.

About this title

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.

Edition details

• Publisher: Springer
• Publication date: 2011
• Language: English
• ISBN 10: 3642182305
• ISBN 13: 9783642182303
• Binding: Paperback
• Number of pages: 192