Martingale solutions and Markov selections for stochastic partial differential equations |
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| Authors: | Benjamin Goldys,Michael Rö ckner,Xicheng Zhang |
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| Affiliation: | 1. School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia;2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany;3. Departments of Mathematics and Statistics, Purdue University, W. Laffayette, IN, 47907, USA;4. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
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| Abstract: | We present a general framework for solving stochastic porous medium equations and stochastic Navier–Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 691–708] and Flandoli–Romito [F. Flandoli, N. Romito, Markov selections for the 3D stochastic Navier–Stokes equations, Probab. Theory Related Fields 140 (2008) 407–458], we also study the existence of Markov selections for stochastic evolution equations in the absence of uniqueness. |
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| Keywords: | Markov selection Martingale solution Stochastic porous medium equation Stochastic Navier&ndash Stokes equation |
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