Impulse control of stochastic Navier–Stokes equations

• Published in: Nonlinear analysis Vol. 52; no. 2; pp. 357 - 381
• Main Authors: Menaldi, J.L., Sritharan, S.S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2003; Elsevier
• Subjects: Calculus of variations and optimal control; Dynamic programming; Exact sciences and technology; Impulse control; Mathematical analysis; Mathematics; Partial differential equations; Sciences and techniques of general use; Stochastic Navier–Stokes equation; Stochastic optimal control; Variational data assimilation; Variational inequality; Impulse control; Stochastic Navier–Stokes equation; Dynamic programming; Variational inequality; Stochastic optimal control; Variational data assimilation; Markov process; Markov Feller process; Probabilistic approach; Fluid dynamics; Sobolev space; Semigroup; Partial differential equation; Stochastic integral; Gaussian process; Navier Stokes equation; Optimal control; Multidimensional model; Stochastic control; Data assimilation; Stochastic equation
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/S0362-546X(01)00722-2

Optimal control theory of fluid dynamics has numerous applications such as aero/hydrodynamic control, combustion control, Tokomak magnetic fusion as well as ocean and atmospheric prediction. During the past decade several fundamental advances have been made by a number of researchers as documented in Sritharan. In this paper we develop a new direction to this subject, namely we mathematically formulate and resolve impulse and stopping time problems. Impulse control of Navier-Stokes equations has significance beyond control theory. In fact, in optimal weather prediction the task of updating the initial data optimally at strategic times can be reformulated precisely as an impulse control problem for the primitive cloud equations (which consist of the Navier-Stokes equation coupled with temperature and species evolution equations.