Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise

Röckner M, Zhu R, Zhu X (2014)
Stochastic Processes and their Applications 124(5): 1974-2002.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications our main results are applied to various types of SPDE such as stochastic reaction diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE. (C) 2014 Elsevier B.V. All rights reserved.
Stichworte
Surface growth models; Navier-Stokes equation; Fractional Burgers; equation; Quasi-geostrophic equation; Stochastic fractional partial differential equation; Local existence and; uniqueness; Blow up
Erscheinungsjahr
2014
Zeitschriftentitel
Stochastic Processes and their Applications
Band
124
Ausgabe
5
Seite(n)
1974-2002
ISSN
0304-4149
Page URI
https://pub.uni-bielefeld.de/record/2677363

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Röckner M, Zhu R, Zhu X. Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. Stochastic Processes and their Applications. 2014;124(5):1974-2002.
Röckner, M., Zhu, R., & Zhu, X. (2014). Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. Stochastic Processes and their Applications, 124(5), 1974-2002. doi:10.1016/j.spa.2014.01.010
Röckner, M., Zhu, R., and Zhu, X. (2014). Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. Stochastic Processes and their Applications 124, 1974-2002.
Röckner, M., Zhu, R., & Zhu, X., 2014. Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. Stochastic Processes and their Applications, 124(5), p 1974-2002.
M. Röckner, R. Zhu, and X. Zhu, “Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise”, Stochastic Processes and their Applications, vol. 124, 2014, pp. 1974-2002.
Röckner, M., Zhu, R., Zhu, X.: Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. Stochastic Processes and their Applications. 124, 1974-2002 (2014).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise”. Stochastic Processes and their Applications 124.5 (2014): 1974-2002.