Abstract
We prove global existence for the one-dimensional cubic nonlinear Schrödinger equation in modulation spaces Mp,p′ for p sufficiently close to 2. In contrast to known results, [9] and [14], our result requires no smallness condition on initial data. The proof adapts a splitting method inspired by work of Vargas–Vega, Hyakuna–Tsutsumi and Grünrock to the modulation space setting and exploits polynomial growth of the free Schrödinger group on modulation spaces.
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