Stochastic Two-Dimensional Hydrodynamical Systems: Wong-Zakai Approximation and Support Theorem |
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| Authors: | Igor Chueshov Annie Millet |
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| Institution: | 1. Department of Mechanics and Mathematics , Kharkov National University , Kharkov, Ukraine chueshov@univ.kharkov.ua;3. SAMM, EA 4543 Université Paris 1, Centre Pierre Mendès France , Paris, France and Laboratoire PMA (UMR 7599) |
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| Abstract: | We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier–Stokes equations, 2D MHD models and 2D magnetic Bénard problems as well as some shell models of turbulence. Our main result describes the support of the distribution of solutions. Both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process. |
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| Keywords: | Bénard convection Hydrodynamical models MHD Shell models of turbulence Stochastic PDEs Support theorem Wong–Zakai approximation |
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