Local existence, global existence, and scattering for the nonlinear Schrödinger equation
Thierry Cazenave, Ivan Naumkin
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Source: Crossref
Published: Feb 20, 2017
DOI: 10.1142/s0219199716500383
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In this paper, we construct for every [Formula: see text] and [Formula: see text] a class of initial values [Formula: see text] for which there exists a local solution of the nonlinear Schrödinger equation [Formula: see text] on [Formula: see text] with the initial condition [Formula: see text]. Moreover, we construct for every [Formula: see text] a class of (arbitrarily large) initial values for which there exists a global solution that scatters as [Formula: see text].
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