Random Perturbation of PDEs and Fluid Dynamic Models

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

  • Franco Flandoli
Part of the Lecture Notes in Mathematics book series (LNM, 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

  • Franco Flandoli
    • 1
  1. 1.Department of Applied MathematicsUniversity of PisaPisaItaly

Bibliographic information

  • 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
  • Print ISBN 978-3-642-18230-3
  • Online ISBN 978-3-642-18231-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692