Stochastic 2-D Navier-Stokes equation

Applied Mathematics and Optimization

Volumn 46, Issue 1, 2002, Pages 31-53

  Menaldi, Jose Luis ^a   Sritharan, Sivaguru S ^b  

^a WAYNE STATE UNIVERSITY   (United States)

^b Space and Naval Warfare Systems Center Pacific   (United States)

Author keywords

Markov Feller semigroup; Maximal monotone operator; Stochastic differential equations; Stochastic Navier Stokes equation

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; MAXIMUM PRINCIPLE; NAVIER STOKES EQUATIONS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; THEOREM PROVING; TWO DIMENSIONAL;

LIONS-PRODI SOLUTION; MARKOV-FELLER SEMIGROUP; MAXIMAL MONOTONE OPERATOR; STOCHASTIC DIFERENTIAL EQUATION;

STOCHASTIC PROGRAMMING;

EID: 0141973204     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00245-002-0734-6     Document Type: Article

References (23)

1. Adams RA (1975) Sobolev Spaces, Academic Press, New York
2. Barbu V, Sritharan SS (2001) Flow invariance preserving feedback controllers for the Navier-Stokes equation, J Math Anal Appl 255:281-307
3. Bensoussan A (1995) Stochastic Navier-Stokes equations, Acta Appl Math 38:267-304
4. Bensoussan A, Temam R (1973) Equations stochastique du type Navier-Stokes, J Funct Anal 13:195-222
5. Capinski M, Cutland NJ (1995) Nonstandard Methods for Stochastic Fluid Mechanics, World Scientific, Singapore
6. Chandrasekhar S (1989) Stochastic, Statistical and Hydromagnetic Problems in Physics and Astronomy, Selected Papers, Vol 3, University of Chicago Press, Chicago
7. Constantin P, Foias C (1988) Navier-Stokes Equations, University of Chicago Press, Chicago
8. Da Prato G, Zabczyk J (1996) Ergodicity for Infinite Dimensional Systems, Cambridge University Press, Cambridge
9. Da Veiga HB (1987) Existence and asymptotic behavior for strong solutions of Navier-Stokes equations in the whole space, Indiana Univ Math J 36:149-156
10. Flandoli F, Gatarek D (1995) Martingale and stationary solutions for the stochastic Navier-Stokes equation, Probab Theory Rel Fields 102:367-391
11. Gyongy I, Krylov NV (1982) On stochastic equations with respect to semimartingales: Itô formula in Banach spaces, Stochastics 6:153-173
12. Ladyzhenskaya OA (1969) The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York
13. Lions JL (1969) Quelque méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris
14. Lions JL, Prodi G (1959) Une théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2, CR Acad Sci Paris 248:3519-3521
15. Menaldi JL, Sritharan SS (2002) Impulse control of stochastic Navier-Stokes equations, Nonlinear Anal Ser A, to appear
16. Minty GJ (1962) Monotone (nonlinear) operators in Hilbert spaces, Duke Math J 29:341-346
17. Novikov EA (1965) Functionals and random force method in turbulence theory, Soviet Phys JETP 20:1290-1294
18. Pardoux E (1979) Stochastic partial differential equations and filtering of diffusion processes, Stochastics 6:127-167
19. Schmalfuss B (1997) Qualitative properties for the stochastic Navier-Stokes equation, Nonlinear Anal 28:1545-1563
20. Sritharan SS (2000) Deterministic and stochastic control of Navier-Stokes equation with linear, monotone and hyperviscosities, Appl Math Optim 41:255-308
21. Temam R (1995) Navier-Stokes Equations and Nonlinear Functional Analysis (second edition), CBMS-NSF 66, SIAM, Philadelphia, PA
22. Vishik MJ, Fursikov AV (1988) Mathematical Problems in Statistical Hydromechanics, Kluwer, Dordrecht
23. W. von Wahl (1985) The Equations of Navier-Stokes and Abstract Parabolic Equations, Vieweg, Braunschweig