Dynamic programming for the stochastic Navier-Stokes equations
Da Prato, Giuseppe ; Debussche, Arnaud
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000), p. 459-475 / Harvested from Numdam
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Publié le : 2000-01-01
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     author = {Da Prato, Giuseppe and Debussche, Arnaud},
     title = {Dynamic programming for the stochastic Navier-Stokes equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {34},
     year = {2000},
     pages = {459-475},
     mrnumber = {1765670},
     zbl = {0953.76016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2000__34_2_459_0}
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Da Prato, Giuseppe; Debussche, Arnaud. Dynamic programming for the stochastic Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 459-475. http://gdmltest.u-ga.fr/item/M2AN_2000__34_2_459_0/

[1] F. Abergel and R. Temam, On some control problems in fluid mechanics. Theor. and Comp. Fluid Dynamics 1 (1990) 303-325. | Zbl 0708.76106

[2] V. Barbu and S. Sritharan, H∞-control theory of fluids dynamics. Proc. R. Soc. Lond. A 454 (1998) 3009-3033. | MR 1658234 | Zbl 0919.93026

[3] T. Bewley, P. Moin and R. Temam, Optimal and robust approaches for linear and nonlinear regulartion problems in fluid mechanics, AIAA 97-1872, 28th AIAA Fluid Dynamics Conference and 4th AIAA Shear Flow Control Conference (1997).

[4] P. Cannarsa and G. Da Prato, Some results on nonlinear optimal control problems and Hamilton-Jacobi equations in infinite dimensions. J. Funct. Anal. 90 (1990) 27-47. | MR 1047576 | Zbl 0717.49022

[5] P. Cannarsa and G. Da Prato, Direct solution of a second order Hamilton-Jacobi equation in Hilbert spaces, in: Stochastic partial differential equations and applications, G. da Prato and L. Tubaro Eds, Pitman Research. Notes in Mathernatics Series n° 268 (1992) pp. 72-85. | MR 1222689 | Zbl 0805.49016

[6] S. Cerrai, Optimal control problem for stochastic reaction-diffusion systems with non Lipschitz coefficients (to appear). | MR 1825865 | Zbl 0987.60073

[7] H. Choi, R. Temam, P. Moin and J. Kim, Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253 (1993) 509-543. | MR 1233904 | Zbl 0810.76012

[8] G. Da Prato and A. Debussche, Differentiability of the transition semigroup of stochastic Burgers equation. Rend. Acc. Naz. Lincei, s.9, v.9 (1998) 267-277. | MR 1722786 | Zbl 0931.37036

[9] G. Da Prato and A. Debussche, Dynamic Programming for the stochastic Burgers equations. Annali di Mat. Pura ed. Appl. (to appear). | MR 1849384 | Zbl 1016.49024

[10] G. Da Prato and J. Zabczyk, Differentiability of the Feynman-Kac semigroup and a control application. Rend. Mat. Acc. Lincei s.9, v.8 (1997) 183-188. | MR 1611613 | Zbl 0910.93025

[11] H. Fattorini and S. Sritharan, Existence of optimal controls for viscous flow problems. Proc. R. Soc. Lond. A 439 (1992) 81-102. | MR 1188854 | Zbl 0786.76063

[12] F. Gozzi, Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem. Commun. in partial differential equations 20 (1995) 775-826. | MR 1326907 | Zbl 0842.49021

[13] F. Gozzi, Global Regular Solutions of Second Order Hamilton-Jacobi Equations in Hilbert spaces with locally Lipschitz nonlinearities. J. Math. Anal. Appl. 198 (1996) 399-443. | MR 1376272 | Zbl 0858.35129

[14] P. L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution. Acta Math 161 (1988) 243-278. Part II : Optimal control of Zakai's equation, in Stochastic partial differential equations and applications, G. da Prato and L. Tubaro Eds, Lecture Notes in Mathematics No. 1390, Springer-Verlag (1990) 147-170. Part III: Uniqueness of viscosity solutions for general second order equations. J. Funct. Anal. 86 (1991) 1-18. | MR 971797 | Zbl 0757.93083

[15] S. Sritharan, Dynamic programming of the Navier-Stokes equations. Syst. Cont. Lett. 16 (1991) 299-307. | MR 1102218 | Zbl 0737.49021

[16] S. Sritharan, An introduction to determimstic and stochastic control of viscous flow, in Optimal control of viscous flows, p. 1-42, SIAM, Philadelphia, S. Sritharan Ed. | MR 1632419

[17] A. Swiech, Viscosity solutions of fully nonlinear partial differential equations with "unbounded" terms in infinite dimensions, Ph D thesis, University of Cahforma at Santa Barbara (1993).

[18] R. Temam, T. Bewley and P. Moin, Control of turbulent flows, Proc of the 18th IFIP TC7, Conf. on System modelling ond optimization, Detroit, Michigan (1997). | Zbl 0925.93417

[19] R. Temam, The Navier-Stokes equation, North-Holland (1977).