Flandoli Random Perturbation of PDEs and Fluid Dynamic Models
Erscheinungsjahr 2011
ISBN: 978-3-642-18231-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
École d’Été de Probabilités de Saint-Flour XL – 2010
E-Book, Englisch, 182 Seiten, Web PDF
Reihe: Mathematics and Statistics
ISBN: 978-3-642-18231-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
1. Introduction to Uniqueness and Blow-up.- 2. Regularization by Additive Noise.- 3. Dyadic Models.- 4. Transport Equation.- 5. Other Models. Uniqueness and Singularities
