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© 2011

Random Perturbation of PDEs and Fluid Dynamic Models

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

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2015)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 2015)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Franco Flandoli
    Pages 1-16
  3. Franco Flandoli
    Pages 17-69
  4. Franco Flandoli
    Pages 71-99
  5. Franco Flandoli
    Pages 101-131
  6. Franco Flandoli
    Pages 133-159
  7. Back Matter
    Pages 161-176

About this book

Introduction

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.

Keywords

60H15, 60H10, 60J65, 35R60, 35Q35, 35B44, 76B03 Blow-up Stochastic Fluid Dynamics Stochastic Partial Differential Equations Uniqueness

Authors and affiliations

  1. 1.Department of Applied MathematicsUniversity of PisaPisaItaly

Bibliographic information

  • Book Title Random Perturbation of PDEs and Fluid Dynamic Models
  • Book Subtitle École d’Été de Probabilités de Saint-Flour XL – 2010
  • Authors Franco Flandoli
  • Series Title Lecture Notes in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-18231-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-642-18230-3
  • eBook ISBN 978-3-642-18231-0
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages X, 182
  • Number of Illustrations 10 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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