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Random Perturbation of PDEs and Fluid Dynamic Models [electronic resource] :École d’Été de Probabilités de Saint-Flour XL – 2010 / by Franco Flandoli.

by Flandoli, Franco [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 2015Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.Description: IX, 176p. 10 illus. online resource.ISBN: 9783642182310.Subject(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic ProcessesDDC classification: 519.2 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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1. Introduction to Uniqueness and Blow-up -- 2. Regularization by Additive Noise -- 3. Dyadic Models -- 4. Transport Equation -- 5. Other Models. Uniqueness and Singularities.

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.

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