Random Perturbation of PDEs and Fluid Dynamic Models

École d’Été de Probabilités de Saint-Flour XL – 2010

von Franco Flandoli

182 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783642182303
• Sprache: Englisch
• Erscheinungsdatum: 11.03.2011
• Genre: Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
• Verlag: Springer Berlin