A Wentzellâ€“Freidlin type large deviation principle is established for the two-dimensional Navierâ€“Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The largeâ€¦ (More)

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navierâ€“Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of theâ€¦ (More)

In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach,â€¦ (More)

We study the infinite dimensional second-order Hamilton-Jacobi-Bellman equations associated to the feedback synthesis of stochastic Navier-Stokes equation forced by space-time white noise. Uniquenessâ€¦ (More)

In this paper we establish the local exact internal controllability of steady state solutions for the Navierâ€“Stokes equations in threeâ€“ dimensional bounded domains, with the Navier slip boundaryâ€¦ (More)

Optimal control theory of viscous flow has many important applications in engineering science. During the past few years several fundamental advances have been reported for flow control problems withâ€¦ (More)

We study the n-dimensional nonlinear filtering problem for jumpdiffusion processes. The optimal filter is derived for the case when the observations are continuous. A proof of uniqueness is presentedâ€¦ (More)

The stochastic Navier-Stokes equation is a well accepted model for atmospheric, aero and ocean dynamics. Chandrasekhar [5] and Novikov [14] first studied the Navier-Stokes equation with externalâ€¦ (More)

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, orâ€¦ (More)

Optimal control theory of distributed parameter systems is a rapidly developing subject [3,10,9,11]. So far the impact of this growth to continuum mechanics has been essentially in the branch ofâ€¦ (More)