- 338 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Mathematics of Two-Dimensional Turbulence
About this book
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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Information
Table of contents
- Cover
- Mathematics of Two-Dimensional Turbulence
- Title
- Copyright
- Dedication
- Contents
- Preface
- 1 Preliminaries
- 2 Two-dimensional Navier–Stokes equations
- 3 Uniqueness of stationary measure
- 4 Ergodicity and limiting theorems
- 5 Inviscid limit
- 6 Miscellanies
- Appendix
- Solutions to selected exercises
- Notation and conventions
- References
- Index
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Yes, you can access Mathematics of Two-Dimensional Turbulence by Sergei Kuksin,Armen Shirikyan in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over 1.5 million books available in our catalogue for you to explore.