Cauchy Problem for Stochastic Nonlinear Schrödinger Equation with Nonlinear Energy-Critical Damping

Lijun Miao and Linlin Qiu ()
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Lijun Miao: School of Mathematics, Liaoning Normal University, Dalian 116029, China
Linlin Qiu: School of Mathematics, Liaoning Normal University, Dalian 116029, China

Mathematics, 2024, vol. 12, issue 16, 1-12

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 H 1 ( R d ) 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.

Keywords: stochastic nonlinear Schrödinger equation; global well-posedness; energy-critical damping; additive noise; energy space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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