Space-time analytic smoothing effect for the cubic nonlinear Schrödinger equations without pseudo-conformal invariance

Gaku Hoshino ()
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Gaku Hoshino: Tokyo Denki University

Partial Differential Equations and Applications, 2022, vol. 3, issue 1, 1-21

Abstract: Abstract We study the global Cauchy problem for the cubic nonlinear Schrödinger equations in space dimensions $$n\ge 1.$$ n ≥ 1 . In particular we prove the space-time analytic smoothing effect for the cubic nonlinear Schrödinger equations. If $$n=2$$ n = 2 then the cubic nonlinear Schrödinger equation is invariant under the pseudo-conformal transform and in this case the space-time analytic smoothing effect has been studied in Hoshino and Ozawa (Nonlinear Differ Equ Appl 23:3, 2016) by applying the generator of pseudo-conformal transform. Our main purpose of this study is to extend the result obtained in previous study.

Keywords: Nonlinear Schrödinger equations; Space-time analytic smoothing effect; Pseudo-conformal power; 35Q55 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00151-w

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