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Mathematics - Probability Theory and Stochastic Processes | Random Perturbation of PDEs and Fluid Dynamic Models - École d’Été de Probabilités de Saint-Flour

Random Perturbation of PDEs and Fluid Dynamic Models

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

Flandoli, Franco

2011, IX, 176p. 10 illus..

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  • About this book

  • Explores why SPDEs sometimes perform better than PDEs
  • Presents non-traditional research directions in SPDE theory
  • Investigates the interaction between noise and uniqueness or singularities
  • Includes special techniques for stochastic fluid dynamic models

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.

Content Level » Research

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

Related subjects » Probability Theory and Stochastic Processes

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