Affiliation:
1. School of Mathematics, Liaoning Normal University, Dalian 116029, China
Abstract
We consider the Cauchy problem for the stochastic nonlinear Schrödinger equation augmented by nonlinear energy-critical damping term arising in nonlinear optics and quantum field theory. Through examining the behavior of the momentum and energy functionals, we almost surely prove the existence and uniqueness of global solutions with continuous H1(Rd) valued paths. The results cover either defocusing nonlinearity in the full energy critical and subcritical range of exponents or focusing nonlinearity in the full subcritical range, as in the deterministic case.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Universities of the Educational Department of Liaoning Provincial of China
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