SPDE in Hydrodynamics: Recent Progress and Prospects: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005

by Sergio Albeverio, Franco Flandoli, Yakov G. Sinai

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

182 pages, Paperback

First published April 14, 2008

About the author

Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.

He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.