@article{M2AN_2000__34_2_459_0, author = {Da Prato, Giuseppe and Debussche, Arnaud}, title = {Dynamic programming for the stochastic {Navier-Stokes} equations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {459--475}, publisher = {Dunod}, address = {Paris}, volume = {34}, number = {2}, year = {2000}, zbl = {0953.76016}, mrnumber = {1765670}, language = {en}, url = {http://archive.numdam.org/item/M2AN_2000__34_2_459_0/} }

TY - JOUR AU - Da Prato, Giuseppe AU - Debussche, Arnaud TI - Dynamic programming for the stochastic Navier-Stokes equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2000 SP - 459 EP - 475 VL - 34 IS - 2 PB - Dunod PP - Paris UR - http://archive.numdam.org/item/M2AN_2000__34_2_459_0/ LA - en ID - M2AN_2000__34_2_459_0 ER -

%0 Journal Article %A Da Prato, Giuseppe %A Debussche, Arnaud %T Dynamic programming for the stochastic Navier-Stokes equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2000 %P 459-475 %V 34 %N 2 %I Dunod %C Paris %U http://archive.numdam.org/item/M2AN_2000__34_2_459_0/ %G en %F M2AN_2000__34_2_459_0

Da Prato, Giuseppe; Debussche, Arnaud. Dynamic programming for the stochastic Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 (2000) no. 2, pp. 459-475. http://archive.numdam.org/item/M2AN_2000__34_2_459_0/

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

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

and ,[3] 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).

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

and ,[5] 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 | Zbl

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

,[7] Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253 (1993) 509-543. | MR | Zbl

, , and ,[8] Differentiability of the transition semigroup of stochastic Burgers equation. Rend. Acc. Naz. Lincei, s.9, v.9 (1998) 267-277. | EuDML | MR | Zbl

and ,[9] Dynamic Programming for the stochastic Burgers equations. Annali di Mat. Pura ed. Appl. (to appear). | MR | Zbl

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

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

and ,[12] 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 | Zbl

,[13] 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 | Zbl

,[14] 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 | Zbl

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

,[16] 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

,[17] 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] Control of turbulent flows, Proc of the 18th IFIP TC7, Conf. on System modelling ond optimization, Detroit, Michigan (1997). | Zbl

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

,