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References (26)
-
V. Barbu, S. Sritharan (2001)
Flow Invariance Preserving Feedback Controllers for the Navier–Stokes EquationJournal of Mathematical Analysis and Applications, 255
-
川口 光年 (1964)
O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円., 19
-
E. Pardouxt (1980)
Stochastic partial differential equations and filtering of diffusion processes, 3
-
I. Gyöngy, N. Krylov (1980)
On stochastic equations with respect to semimartingales I.Stochastics An International Journal of Probability and Stochastic Processes, 4
-
(1959)
Une théorème d’existence et unicité dans les équations de Navier–Stokes en dimension 2, CR -
J. Menaldi, S. Sritharan (2003)
Impulse control of stochastic Navier-Stokes equationsNonlinear Analysis-theory Methods & Applications, 52
-
I. Gyöngy, N. Krylov (1982)
On stochastics equations with respect to semimartingales ii. itô formula in banach spaces, 6
-
A. Bensoussan, R. Temam (1973)
Equations stochastiques du type Navier-StokesJournal of Functional Analysis, 13
-
O. Ladyzhenskaya, R. Silverman, J. Schwartz, J. Romain (1972)
The Mathematical Theory of Viscous Incompressible Flow -
G. Minty (1962)
Monotone (nonlinear) operators in Hilbert spaceDuke Mathematical Journal, 29
-
R. Temam (1977)
Navier-Stokes Equations -
E. Boschi (1971)
Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969;Il Nuovo Cimento B, 5
-
Alain Bensoussan (1995)
Stochastic Navier-Stokes EquationsActa Applicandae Mathematica, 38
-
B. Schmalfuß (1997)
Qualitative properties for the stochastic Navier-Stokes equationNonlinear Analysis-theory Methods & Applications, 28
-
W. Wahl (1985)
The equations of Navier-Stokes and abstract parabolic equations -
S. Chandrasekhar (1989)
Stochastic, statistical, and hydromagnetic problems in physics and astronomy -
E. Novikov (1965)
Functionals and the random-force method in turbulence theoryJournal of Experimental and Theoretical Physics, 20
-
S. Sritharan (2000)
Deterministic and Stochastic Control of Navier—Stokes Equation with Linear, Monotone, and HyperviscositiesApplied Mathematics and Optimization, 41
-
S. Chandrasekhar (1989)
Selected papers of S. Chandrasekhar. Volume 3: Stochastic, statistical, and hydromagnetic problems in physics and astronomy. -
M. Vishik, A. Fursikov (1988)
Mathematical Problems of Statistical Hydromechanics -
(1996)
Ergodicity for Infinite Dimensional Systems -
F. Flandoli, D. Gatarek (1995)
Martingale and stationary solutions for stochastic Navier-Stokes equationsProbability Theory and Related Fields, 102
-
H. Veiga (1985)
Existence and Asymptotic Behavior for Strong Solutions of Navier-Stokes Equations in the Whole SpaceIndiana University Mathematics Journal, 36
-
R. Temam (1995)
Navier–Stokes Equations and Nonlinear Functional Analysis: Second Edition -
R. Temam (1987)
Navier-Stokes Equations and Nonlinear Functional Analysis -
M. Capinski, N. Cutland (1995)
Nonstandard Methods for Stochastic Fluid Mechanics
- Publisher
- Springer Journals
- Copyright
- Copyright © Inc. by 2002 Springer-Verlag New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-002-0734-6
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2002