A Stochastic Nonlinear Schrödinger Equation¶ with Multiplicative Noise
A de Bouard, A Debussche - Communications in mathematical physics, 1999 - Springer
Communications in mathematical physics, 1999•Springer
We study a conservative stochastic nonlinear Schrödinger equation with a multiplicative
noise. We show the global existence and uniqueness of square integrable solutions for
subcritical nonlinearities, the critical exponent being the same, in dimension 1 or 2, as the
critical exponent of the deterministic equation.
noise. We show the global existence and uniqueness of square integrable solutions for
subcritical nonlinearities, the critical exponent being the same, in dimension 1 or 2, as the
critical exponent of the deterministic equation.
Abstract
We study a conservative stochastic nonlinear Schrödinger equation with a multiplicative noise. We show the global existence and uniqueness of square integrable solutions for subcritical nonlinearities, the critical exponent being the same, in dimension 1 or 2, as the critical exponent of the deterministic equation.
Springer
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