Mathematics of Two-Dimensional Turbulence

Nonfiction, Science & Nature, Mathematics, Statistics, Science
Cover of the book Mathematics of Two-Dimensional Turbulence by Sergei Kuksin, Armen Shirikyan, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Sergei Kuksin, Armen Shirikyan ISBN: 9781139579575
Publisher: Cambridge University Press Publication: September 20, 2012
Imprint: Cambridge University Press Language: English
Author: Sergei Kuksin, Armen Shirikyan
ISBN: 9781139579575
Publisher: Cambridge University Press
Publication: September 20, 2012
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book Lectures on Quantum Mechanics by Sergei Kuksin, Armen Shirikyan
Cover of the book The Mechanics of Earthquakes and Faulting by Sergei Kuksin, Armen Shirikyan
Cover of the book Lucan's Egyptian Civil War by Sergei Kuksin, Armen Shirikyan
Cover of the book Global Business Regulation by Sergei Kuksin, Armen Shirikyan
Cover of the book Byzantine Legal Culture and the Roman Legal Tradition, 867–1056 by Sergei Kuksin, Armen Shirikyan
Cover of the book The Politics of Inheritance in Romans by Sergei Kuksin, Armen Shirikyan
Cover of the book Yeats and Modern Poetry by Sergei Kuksin, Armen Shirikyan
Cover of the book Dynamics of Quantised Vortices in Superfluids by Sergei Kuksin, Armen Shirikyan
Cover of the book A Concise History of International Finance by Sergei Kuksin, Armen Shirikyan
Cover of the book The Epilepsy Prescriber's Guide to Antiepileptic Drugs by Sergei Kuksin, Armen Shirikyan
Cover of the book Democratic Policymaking by Sergei Kuksin, Armen Shirikyan
Cover of the book Introduction to Plasma Physics by Sergei Kuksin, Armen Shirikyan
Cover of the book Japan's Castles by Sergei Kuksin, Armen Shirikyan
Cover of the book Introduction to Computable General Equilibrium Models by Sergei Kuksin, Armen Shirikyan
Cover of the book Credit Risk by Sergei Kuksin, Armen Shirikyan
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy