A stochastic nonlinear Schrodinger equation with multiplicative noise

Authors
de Bouard, A Debussche, A
Citation
A. De Bouard et A. Debussche, A stochastic nonlinear Schrodinger equation with multiplicative noise, COMM MATH P, 205(1), 1999, pp. 161-181
Citations number
11
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
205
Issue
1
Year of publication
1999
Pages
161 - 181
Database
ISI
SICI code
0010-3616(199908)205:1<161:ASNSEW>2.0.ZU;2-#
Abstract
We study a conservative stochastic nonlinear Schrodinger equation with a mu ltiplicative noise. We show the global existence and uniqueness of square i ntegrable solutions for subcritical nonlinearities, the critical exponent b eing the same, in dimension 1 or 2, as the critical exponent of the determi nistic equation.