Flandoli, Franco.
Random Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 / [electronic resource] : by Franco Flandoli. - IX, 176p. 10 illus. online resource. - Lecture Notes in Mathematics, 2015 0075-8434 ; . - Lecture Notes in Mathematics, 2015 .
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.
9783642182310
10.1007/978-3-642-18231-0 doi
Mathematics.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Random Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 / [electronic resource] : by Franco Flandoli. - IX, 176p. 10 illus. online resource. - Lecture Notes in Mathematics, 2015 0075-8434 ; . - Lecture Notes in Mathematics, 2015 .
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.
9783642182310
10.1007/978-3-642-18231-0 doi
Mathematics.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2