Mathematics of Two-Dimensional Turbulence

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.

Author: Sergei Kuksin
Publisher: Cambridge University Press
Published: 09/20/2012
Pages: 336
Binding Type: Hardcover
Weight: 1.35lbs
Size: 9.10h x 6.00w x 0.90d
ISBN: 9781107022829

About the Author
Kuksin, Sergei: - Sergei Kuksin is a Professor in the Centre Mathématiques Laurent Schwartz at École Polytechnique in Palaiseau, France.