TY - JOUR
T1 - Martingale solutions and Markov selections for stochastic partial differential equations
AU - Goldys, Benjamin
AU - Röckner, Michael
AU - Zhang, Xicheng
PY - 2009/5
Y1 - 2009/5
N2 - 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.
AB - 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.
KW - Markov selection
KW - Martingale solution
KW - Stochastic Navier-Stokes equation
KW - Stochastic porous medium equation
UR - http://www.scopus.com/inward/record.url?scp=62249153217&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2008.08.009
DO - 10.1016/j.spa.2008.08.009
M3 - Article
AN - SCOPUS:62249153217
SN - 0304-4149
VL - 119
SP - 1725
EP - 1764
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 5
ER -