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Stochastic control of tidal dynamics equation with Lévy noise. (English) Zbl 1420.35220
Summary: In this work we first present the existence, uniqueness and regularity of the strong solution of the tidal dynamics model perturbed by Lévy noise. Monotonicity arguments have been exploited in the proofs. We then formulate a martingale problem of D. W. Stroock and S. R. S. Varadhan [Multidimensional diffusion processes. Berlin, Heidelberg, New York: Springer (1979; Zbl 0426.60069)] associated to an initial value control problem and establish existence of optimal controls.
MSC:
35Q35 PDEs in connection with fluid mechanics
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D55 Flow control and optimization for incompressible viscous fluids
35D35 Strong solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35B65 Smoothness and regularity of solutions to PDEs
93E20 Optimal stochastic control
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