Optimal Control for Two-Dimensional Stochastic Navier-Stokes Equations

Loeb space methods are used to prove the existence of an optimal control for the two-dimensional stochastic Navier--Stokes equations in a variety of settings—including that of control based on digital observations of the evolution of the solution.

[1]  L. Rogers Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[2]  Existence of global stochastic flow and attractors for Navier–Stokes equations , 1999 .

[3]  Sri Sritharan,et al.  Deterministic and Stochastic Control of Navier—Stokes Equation with Linear, Monotone, and Hyperviscosities , 2000 .

[4]  H. Lisei Existence of optimal and ε-optimal controls for the stochastic Navier-Stokes equation , 2002 .

[5]  G. Prato,et al.  DYNAMIC PROGRAMMING FOR THE STOCHASTIC NAVIER-STOKES EQUATIONS , 2000 .

[6]  S. Albeverio Nonstandard Methods in Stochastic Analysis and Mathematical Physics , 1986 .

[7]  N. Cutland Infinitesimal methods in control theory: Deterministic and stochastic , 1986 .

[8]  H. Keisler,et al.  Global Attractors for 3-Dimensional Stochastic Navier–Stokes Equations , 2004 .

[9]  N. Cutland On the existence of solutions to stochastic differential equations on Loeb spaces , 1982 .

[10]  S. Sritharan,et al.  Bellman equations associated to the optimal feedback control of stochastic Navier‐Stokes equations , 2005 .

[11]  ATTRACTORS AND NEO-ATTRACTORS FOR 3D STOCHASTIC NAVIER–STOKES EQUATIONS , 2005 .

[12]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[13]  J. Menaldi,et al.  Impulse control of stochastic Navier-Stokes equations , 2003 .

[14]  David A. Ross Loeb Measure and Probability , 1997 .

[15]  Marek Capiński,et al.  Nonstandard Methods for Stochastic Fluid Mechanics , 1995 .

[16]  Marek Capiński,et al.  Stochastic Navier-Stokes equations , 1991 .

[17]  A. Ichikawa Stability of semilinear stochastic evolution equations , 1982 .

[18]  R. Temam Navier-Stokes Equations , 1977 .