عنوان

Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions /

3037190213

9783037190210

b738892

Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions /

[Book]

Sergei B. Kuksin.

Zürich :

European Mathematical Society,

©2006.

ix, 92 pages :

illustrations ;

24 cm.

Zurich lectures in advanced mathematics

Includes bibliographical references (pages 88-92) and index.

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.

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Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions.

Differentiable dynamical systems.

Differential equations, Partial.

Hydrodynamics.

Navier-Stokes equations.

Differentiable dynamical systems.

Differentiable dynamical systems.

Differential equations, Nonlinear.

Differential equations, Partial.

Hydrodynamics-- Statistical methods.

Hydrodynamics.

Navier-Stokes equations-- Numerical solutions.

Navier-Stokes equations.

Navier-Stokes-Gleichung

Stochastic differential equations.

Strömungsmechanik

Turbulente Strömung

Kuksin, Sergej B.,1955-

20201203235611.0

[Book]

Y