TY - JOUR
T1 - Almost conservation laws for stochastic nonlinear Schrödinger equations
AU - Cheung, Kelvin
AU - Li, Guopeng
AU - Oh, Tadahiro
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/6
Y1 - 2021/6
N2 - In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on R3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.
AB - In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on R3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.
KW - Almost conservation law
KW - Global well-posedness
KW - I-method
KW - Stochastic nonlinear Schrödinger equation
UR - https://www.scopus.com/pages/publications/85099587697
U2 - 10.1007/s00028-020-00659-x
DO - 10.1007/s00028-020-00659-x
M3 - Article
AN - SCOPUS:85099587697
SN - 1424-3199
VL - 21
SP - 1865
EP - 1894
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 2
ER -