Mathematics of Two-Dimensional Turbulence
Mathematics of Two-Dimensional Turbulence
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Résumé
This rigorous study of statistical hydrodynamics and turbulence is ideal for mathematicians and physicists who need to understand the mathematical foundations of the field. It provides the reader with a general overview of existing results and it is a useful source for courses at the graduate level and beyond.
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Mathematics of Two-Dimensional Turbulence by Sergei Kuksin
This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
Sergei Kuksin is a Professor in the Centre Mathématiques Laurent Schwartz at École Polytechnique in Palaiseau, France. Armen Shirikyan is a professor in the mathematics department at the University of Cergy-Pontoise (UCP), France, and served as the Head of Department from April 2008 to August 2012. He gained his PhD from Moscow State University in 1995 and his Habilitation thesis from the University of Paris-Sud in 2003. His current research interests are related to the ergodic theory for randomly forced equations of mathematical physics and controllability of nonlinear PDEs.
| SKU | Non disponible |
| ISBN 13 | 9781107022829 |
| ISBN 10 | 1107022827 |
| Titre | Mathematics of Two-Dimensional Turbulence |
| Auteur | Sergei Kuksin |
| Série | Cambridge Tracts In Mathematics |
| État | Non disponible |
| Éditeur | Cambridge University Press |
| Année de publication | 2012-09-20 |
| Nombre de pages | 336 |
| Note de couverture | La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier. |
| Note | Non disponible |