Conservative stochastic two-dimensional Cahn–Hilliard equation

Röckner M, Yang H, Zhu R (2021)
Annals of Applied Probability 31(3): 1336-1375.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider the stochastic two-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution Y to the shifted equation (1.4). Then X := Y + Z is the unique solution to the stochastic Cahn-Hilliard equation, where Z is the corresponding O-U process. Moreover, we use the Dirichlet form approach in (Probab. Theory Related Fields 89 (1991) 347-386) to construct a probabilistically weak solution to the original equation (1.1) below. By clarifying the precise relation between the two solutions, we also get the restricted Markov uniqueness of the generator and the uniqueness of the martingale solutions to the equation (1.1). Furthermore, we also obtain exponential ergodicity of the solutions.
Stichworte
Stochastic quantization problem; Dirichlet forms; space-time white; noise; Wick power; nonlinear stochastic PDE
Erscheinungsjahr
2021
Zeitschriftentitel
Annals of Applied Probability
Band
31
Ausgabe
3
Seite(n)
1336-1375
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2956278

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Röckner M, Yang H, Zhu R. Conservative stochastic two-dimensional Cahn–Hilliard equation. Annals of Applied Probability. 2021;31(3):1336-1375.
Röckner, M., Yang, H., & Zhu, R. (2021). Conservative stochastic two-dimensional Cahn–Hilliard equation. Annals of Applied Probability, 31(3), 1336-1375. https://doi.org/10.1214/20-AAP1620
Röckner, M., Yang, H., and Zhu, R. (2021). Conservative stochastic two-dimensional Cahn–Hilliard equation. Annals of Applied Probability 31, 1336-1375.
Röckner, M., Yang, H., & Zhu, R., 2021. Conservative stochastic two-dimensional Cahn–Hilliard equation. Annals of Applied Probability, 31(3), p 1336-1375.
M. Röckner, H. Yang, and R. Zhu, “Conservative stochastic two-dimensional Cahn–Hilliard equation”, Annals of Applied Probability, vol. 31, 2021, pp. 1336-1375.
Röckner, M., Yang, H., Zhu, R.: Conservative stochastic two-dimensional Cahn–Hilliard equation. Annals of Applied Probability. 31, 1336-1375 (2021).
Röckner, Michael, Yang, Huanyu, and Zhu, Rongchan. “Conservative stochastic two-dimensional Cahn–Hilliard equation”. Annals of Applied Probability 31.3 (2021): 1336-1375.

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