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Random Perturbation of PDEs and Fluid Dynamic Models By Franco Flandoli

Random Perturbation of PDEs and Fluid Dynamic Models by Franco Flandoli

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Summary

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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Random Perturbation of PDEs and Fluid Dynamic Models Summary

Random Perturbation of PDEs and Fluid Dynamic Models: Ecole d'Ete de Probabilites de Saint-Flour XL - 2010 by Franco Flandoli

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.

Table of 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

Additional information

NLS9783642182303
9783642182303
3642182305
Random Perturbation of PDEs and Fluid Dynamic Models: Ecole d'Ete de Probabilites de Saint-Flour XL - 2010 by Franco Flandoli
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2011-03-11
182
N/A
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