Martingale solutions and Markov selections for stochastic partial differential equations
By Ben Goldys, Michael Röckner, Xicheng Zhang. 2009
80 citations recorded by the source corpus.
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.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/32318f2a7d13d75b86de8585235f34e9fb7011dd
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In Finance
- Tusheng Zhang
- Xicheng Zhang
- Michael Röckner
- Shijie Shang
- Wei Liu
- Xiangchan Zhu
- Rongchan Zhu
- Martina Hofmanov'a
In Mathematical Physics
- Tusheng Zhang
- Shijie Shang
- Michael Röckner
- Xicheng Zhang
- Xiangchan Zhu
- Rongchan Zhu
- Martina Hofmanov'a
- Feng-Yu Wang
Citations in the corpus
- Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “Please see [25, 23, 11, 30, 12] for SPDEs with generalized coercivity conditions or Lyapunov conditions, [7, 31, 18] for SPDEs driven by Levy noise, [13] for martingale solutions of SPDEs, and [3] for stochastic porous media equations as well as other references.”
- On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations (2020, background): “Regarding the point (iv), we recall that applications of Krylov’s Markov selection to SPDEs can be found in [5, 30, 32].”
- Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations (2010, background): “[ 13 , 15]). But the uniqueness is open, and one only knows the existence of a locally unique strong solution (cf.”