Mathematics of Two-Dimensional Turbulence Sergei Kuksin

ISBN: 9781107022829

Published: November 12th 2012

Hardcover

336 pages


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Mathematics of Two-Dimensional Turbulence  by  Sergei Kuksin

Mathematics of Two-Dimensional Turbulence by Sergei Kuksin
November 12th 2012 | Hardcover | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 336 pages | ISBN: 9781107022829 | 4.58 Mb

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 fluidsMoreThis 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 fluids 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.



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