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Sergej B. Kuksin
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Mathematics of Two-Dimensional Turbulence (Cambridge Tracts in Mathematics, Series Number 194) 1st Edition

by Sergei Kuksin (Author), Armen Shirikyan (Author)
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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.
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  1. ISBN-10
    041561807X
  2. ISBN-13
    978-0719571787
  3. Edition
    1st
  4. Publisher
    Cambridge University Press
  5. Publication date
    November 12, 2012
  6. Part of series
    Cambridge Tracts in Mathematics
  7. Language
    English
  8. Dimensions
    6.5 x 1 x 9.5 inches
  9. Print length
    336 pages
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Editorial Reviews

Book Description

Presents recent progress in two-dimensional mathematical hydrodynamics, including rigorous results on turbulence in space-periodic fluid flows.

About the Author

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.

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Sergej B. Kuksin

Sergej B. Kuksin

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  • Mouhamadou SY
    5.0 out of 5 stars Enormément sur la turbulence 2D
    Reviewed in France on February 4, 2015
    Format: HardcoverVerified Purchase
    Très bon livre.
    Rappel de beaucoup de notions (donc pas de grands problèmes de prérequis)
    Clarté dans les arguments les plus subtiles. J'ai adoré ce livre qui parle de beaucoup de choses sur
    la turbulence.
    Report