Random Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 /

• Main Author: Flandoli, Franco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2015
• Subjects: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.
• Physical Description: X, 182 p. 10 illus. online resource.
• ISBN: 9783642182310
• ISSN: 0075-8434 ;

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.