Backward stochastic differential equations associated with the vorticity equations |
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| Authors: | AB Cruzeiro ZM Qian |
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| Institution: | 1. Grupo Física-Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal;2. Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;3. Mathematical Institute, University of Oxford, 24-29 St Giles'', Oxford OX1 3LB, England, United Kingdom |
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| Abstract: | In this paper we derive a non-linear version of the Feynman–Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2. A particular class of terminal values provide, via these probabilistic methods, solutions for the vorticity equation. |
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| Keywords: | Navier&ndash Stokes Vorticity equations Backward SDE |
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