Martingale solutions and Markov selections for stochastic partial differential equations

Benjamin Goldys, Michael Röckner and Xicheng Zhang

Stochastic Processes and their Applications, 2009, vol. 119, issue 5, 1725-1764

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.

Keywords: Markov; selection; Martingale; solution; Stochastic; porous; medium; equation; Stochastic; Navier-Stokes; equation (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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