| Document Type
|
:
|
BL
|
| Record Number
|
:
|
984522
|
| Doc. No
|
:
|
b738892
|
| Main Entry
|
:
|
Kuksin, Sergej B.,1955-
|
| Title & Author
|
:
|
Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions /\ Sergei B. Kuksin.
|
| Publication Statement
|
:
|
Zürich :: European Mathematical Society,, ©2006.
|
| Series Statement
|
:
|
Zurich lectures in advanced mathematics
|
| Page. NO
|
:
|
ix, 92 pages :: illustrations ;; 24 cm.
|
| ISBN
|
:
|
3037190213
|
|
|
:
|
: 9783037190210
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references (pages 88-92) and index.
|
| Contents
|
:
|
Machine derived contents note: 1 Function spaces 1 -- 1. Function spaces for functions of x 1 -- 1.2 Functions of t and x 3 -- 2 The deterministic 2D Navier-Stokes Equation 5 -- 2.1 Leray decomposition 5 -- 2 2 Properties of the nonlinearity B 8 -- 2.3 The existence ald uniqueness theorem 10 -- 2 4 Improving the smoothness of solutions 14 -- 2.5 The NS semigroup 18 -- 2.6 Singular forces 19 -- 2.7 Some hydrodynamical terminology 22 -- 3 Random kick-forces 24 -- 3.1 Ingredients for the constructions 24 -- 3.2 The kicked NSE 25 -- 3.3 Stationary measures 27 -- 3.4 More estimates 28 -- 4 White-forced equations 30 -- I. White in time forces 30 -- 4.2 The white-forced 2D NSE 31 -- 4,3 Estimates for solutions 33 -- 4.4 Stationary measures 36 -- 4.5 High-frequency random kicks 37 -- 5 Preiminaries from measure theory 39 -- 5.1 Weak convergence of measures and Lipschitz-dual distance 39 -- 5.2 Variational distance 40 -- 5.3 Coupling 41 -- 5.4 Kantorovich functionals 42 -- 6 Uniqueness of a stationary measure: kick-forces 43 -- 6.1 The main lemma 43 -- 6.2 Weak solution of (6.1) 5 5 -- 6.3 The theorem ,. 46 -- 6.4 Corollaries from the theorem 50 -- 6.5 3D NSE with small random kicks 51 -- 6.6 Stationary measures and random attractors 52 -- 6 7 Appendix: Summary of the proof of Theorem 6.4 53 -- 7 Uniqueness of a stationary measure: white-forces 56 -- 7.1 The main theorem 56 -- 7.2 Stationary measures for equation, perturbed -- by high frequency kicks 58 -- 8 Ergodicity and the strong law of large numbers 60 -- 9 The martingale approximation and CLT 63 -- 10 The Eulerian limit 66 -- 10.1 White-forces, proportional to the square-root -- of the viscosity 66 -- 10.2 One negative result 71 -- 10.3 Other scalings 73 -- 10.4 Discussion 74 -- 105 Kicked equations 75 -- 11 Balance relations for the white-forced NSE 77 -- 11.1 The balance relations 77 -- 11 2 The co-area form of the balance relations 80.
|
| Subject
|
:
|
Differentiable dynamical systems.
|
| Subject
|
:
|
Differential equations, Partial.
|
| Subject
|
:
|
Hydrodynamics.
|
| Subject
|
:
|
Navier-Stokes equations.
|
| Subject
|
:
|
Differentiable dynamical systems.
|
| Subject
|
:
|
Differentiable dynamical systems.
|
| Subject
|
:
|
Differential equations, Nonlinear.
|
| Subject
|
:
|
Differential equations, Partial.
|
| Subject
|
:
|
Hydrodynamics-- Statistical methods.
|
| Subject
|
:
|
Hydrodynamics.
|
| Subject
|
:
|
Navier-Stokes equations-- Numerical solutions.
|
| Subject
|
:
|
Navier-Stokes equations.
|
| Subject
|
:
|
Navier-Stokes-Gleichung
|
| Subject
|
:
|
Stochastic differential equations.
|
| Subject
|
:
|
Strömungsmechanik
|
| Subject
|
:
|
Turbulente Strömung
|
| Dewey Classification
|
:
|
515.353
|
| LC Classification
|
:
|
QA374.K85 2006
|
| NLM classification
|
:
|
31.81bcl
|
|
|
:
|
31.81.bcl
|
|
|
:
|
SK 540rvk
|