Dynamic Programming of Stochastic 2-D Navier-Stokes Equations Forced by Levy Noise

Manil. T. Mohan; K. Sakthivel; Sivaguru S. Sritharan

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arXiv · 2204.08072

Dynamic Programming of Stochastic 2-D Navier-Stokes Equations Forced by Levy Noise

Manil. T. Mohan·K. Sakthivel·Sivaguru S. Sritharan

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Abstract

In this article, we study optimal feedback control synthesis of stochastic 2D Navier-Stokes equations perturbed Levy type noise with distributed stochastic control process acting on the state equation. We use the dynamic programming approach to solve this control problem which involves the study of second order infinite dimensional Hamilton- Jacobi-Bellman (HJB) equation consisting of an integro-differential operator with Levy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic 2D Navier-Stokes equation, we obtain a smooth solution in weighted function space for the HJB equation and solve the resultant feedback control problem.

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BibTeX RIS

Manil. T. Mohan, K. Sakthivel, Sivaguru S. Sritharan. 2022-04-17. Dynamic Programming of Stochastic 2-D Navier-Stokes Equations Forced by Levy Noise. https://arxiv.org/abs/2204.08072

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