Mathematics of two-dimensional turbulence /
Kuksin, Sergej B., 1955-
Mathematics of two-dimensional turbulence / Sergei Kuksin, Armen Shirikyan. - Cambridge [England] ; New York : Cambridge University Press, 2012. - 1 online resource - Cambridge tracts in mathematics ; 194 . - Cambridge tracts in mathematics ; 194. .
Includes bibliographical references (pages 307-318) and index.
1. Preliminaries -- 2. Two-dimensional Navier-Stokes equations -- 3. Uniqueness of stationary measure and mixing -- 4. Ergodicity and limiting theorems -- 5. Inviscid limit -- 6. Miscellanies -- 7. Appendix -- 8. Solutions to some exercises.
"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"-- "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections also provide brief summaries of the corresponding chapters. In Chapters 3 and 4, our main goal is to justify, for the 2D case, the statistical properties of fluid's velocity"--
English.
9781139569194 (electronic bk.) 1139569198 (electronic bk.) 9781139137119 (electronic bk.) 1139137115 (electronic bk.) 9781139571005 1139571001 9781139572750 (ebook) 113957275X 9781139572750 1139888986 9781139888981 1139579576 9781139579575 1139573527 9781139573528 1139570099 9781139570091
9786613951175
395117 MIL
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Hydrodynamique--Méthodes statistiques.
Turbulence--Mathématiques.
MATHEMATICS--Probability & Statistics--General.
SCIENCE--Mechanics--Fluids.
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Electronic book.
Electronic books.
Electronic books.
QA911 / .K85 2012eb
532/.052701519
Mathematics of two-dimensional turbulence / Sergei Kuksin, Armen Shirikyan. - Cambridge [England] ; New York : Cambridge University Press, 2012. - 1 online resource - Cambridge tracts in mathematics ; 194 . - Cambridge tracts in mathematics ; 194. .
Includes bibliographical references (pages 307-318) and index.
1. Preliminaries -- 2. Two-dimensional Navier-Stokes equations -- 3. Uniqueness of stationary measure and mixing -- 4. Ergodicity and limiting theorems -- 5. Inviscid limit -- 6. Miscellanies -- 7. Appendix -- 8. Solutions to some exercises.
"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"-- "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections also provide brief summaries of the corresponding chapters. In Chapters 3 and 4, our main goal is to justify, for the 2D case, the statistical properties of fluid's velocity"--
English.
9781139569194 (electronic bk.) 1139569198 (electronic bk.) 9781139137119 (electronic bk.) 1139137115 (electronic bk.) 9781139571005 1139571001 9781139572750 (ebook) 113957275X 9781139572750 1139888986 9781139888981 1139579576 9781139579575 1139573527 9781139573528 1139570099 9781139570091
9786613951175
395117 MIL
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Hydrodynamique--Méthodes statistiques.
Turbulence--Mathématiques.
MATHEMATICS--Probability & Statistics--General.
SCIENCE--Mechanics--Fluids.
Hydrodynamics--Statistical methods.
Turbulence--Mathematics.
Electronic book.
Electronic books.
Electronic books.
QA911 / .K85 2012eb
532/.052701519