The stochastic fractional Strichartz estimate and blow-up for Schrödinger equation
arxiv(2023)
摘要
We establish the stochastic Strichartz estimate for the fractional
Schrödinger equation with multiplicative noise. With the help of the
deterministic Strichartz estimates, we prove the existence and uniqueness of a
global solution to the stochastic fractional nonlinear Schrödinger equation
in L^2(ℝ^n). In addition, we also prove a general blow up result by
deriving a localized virial estimate and the generalized Strauss inequality
with a restricted class of initial data.
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