Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach

Barbu V, Röckner M, Zhang D (2014)
Journal of Nonlinear Science 24(3): 383-409.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
We prove well-posedness results for stochastic nonlinear Schrodinger equations with linear multiplicative Wiener noise, including the nonconservative case. Our approach is different from the standard literature on stochastic nonlinear Schrodinger equations. By a rescaling transformation we reduce the stochastic equation to a random nonlinear Schrodinger equation with lower-order terms and treat the resulting equation by a fixed point argument based on generalizations of Strichartz estimates proved by Marzuola et al. (J Funct Anal 255(6):1479-1553, 2008). This approach makes it possible to improve earlier well-posedness results obtained in the conservative case by a direct approach to the stochastic Schrodinger equation. In contrast to the latter, we obtain well-posedness in the full range of admissible exponents in the nonlinear part (where is the dimension of the underlying Euclidean space), i.e., in exactly the same range as in the deterministic case.
Stichworte
Strichartz estimate; Stochastic; Wiener noise
Erscheinungsjahr
2014
Zeitschriftentitel
Journal of Nonlinear Science
Band
24
Ausgabe
3
Seite(n)
383-409
ISSN
0938-8974
Page URI
https://pub.uni-bielefeld.de/record/2685876

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Barbu V, Röckner M, Zhang D. Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science. 2014;24(3):383-409.
Barbu, V., Röckner, M., & Zhang, D. (2014). Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science, 24(3), 383-409. doi:10.1007/s00332-014-9193-x
Barbu, V., Röckner, M., and Zhang, D. (2014). Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science 24, 383-409.
Barbu, V., Röckner, M., & Zhang, D., 2014. Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science, 24(3), p 383-409.
V. Barbu, M. Röckner, and D. Zhang, “Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach”, Journal of Nonlinear Science, vol. 24, 2014, pp. 383-409.
Barbu, V., Röckner, M., Zhang, D.: Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science. 24, 383-409 (2014).
Barbu, Viorel, Röckner, Michael, and Zhang, Deng. “Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach”. Journal of Nonlinear Science 24.3 (2014): 383-409.