Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds Article Swipe
Related Concepts
Mathematics
Uniqueness
Martingale (probability theory)
Nonlinear system
Multiplicative function
Pure mathematics
Multiplicative noise
Mathematical analysis
Applied mathematics
Physics
Computer science
Computer hardware
Signal transfer function
Digital signal processing
Analog signal
Quantum mechanics
Zdzisław Brzeźniak
,
Fabian Hornung
,
Lutz Weis
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.10619
· OA: W4289665956
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.10619
· OA: W4289665956
We prove pathwise uniqueness for solutions of the nonlinear Schrödinger equation with conservative multiplicative noise on compact 3D manifolds. In particular, we generalize the result by Burq, Gérard and Tzvetkov (N. Burq, P. Gérard, and N. Tzvetkov. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. American Journal of Mathematics, 126 (3):569--605, 2004) to the stochastic setting. The proof is based on deterministic and stochastic Strichartz estimates and the Littlewood-Paley decomposition.
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