Martingale solutions and Markov selections for stochastic partial differential equations

Benjamin Goldys; Michael Röckner; Xicheng Zhang

doi:10.1016/j.spa.2008.08.009

Martingale solutions and Markov selections for stochastic partial differential equations

Benjamin Goldys, Michael Röckner^*, Xicheng Zhang

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科研成果: 期刊稿件 › 文章 › 同行评审

52 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1725-1764
页数	40
期刊	Stochastic Processes and their Applications
卷	119
期	5
DOI	https://doi.org/10.1016/j.spa.2008.08.009
出版状态	已出版 - 5月 2009
已对外发布	是

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Goldys, B., Röckner, M., & Zhang, X. (2009). Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications, 119(5), 1725-1764. https://doi.org/10.1016/j.spa.2008.08.009

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title = "Martingale solutions and Markov selections for stochastic partial differential equations",

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keywords = "Markov selection, Martingale solution, Stochastic Navier-Stokes equation, Stochastic porous medium equation",

author = "Benjamin Goldys and Michael R{\"o}ckner and Xicheng Zhang",

year = "2009",

month = may,

doi = "10.1016/j.spa.2008.08.009",

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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

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SN - 0304-4149

VL - 119

SP - 1725

EP - 1764

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5

ER -

Martingale solutions and Markov selections for stochastic partial differential equations

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