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- W3005954743 abstract "An Lp-theory of local and global solutions for the one dimensional nonlinear Schrödinger equations with pure power like nonlinearities is developed. Firstly, twisted local well-posedness results in scaling subcritical Lp-spaces are established for p<2. This extends Zhou's earlier results for the gauge-invariant cubic NLS equation. Secondly, by a similar functional framework, the global well-posedness for small data in critical Lp-spaces is proved, and as an immediate consequence, Lp′-Lp type decay estimates for the global solutions are derived, which are well known for the global solutions to the corresponding linear Schrödinger equation. Finally, global well-posedness results for gauge-invariant equations with large Lp-data are proved, which improve earlier existence results, and from which it is shown that the global solution u has a smoothing effect in terms of spatial integrability at any large time. Various Strichartz type inequalities in the Lp-framework including linear weighted estimates and bi-linear estimates for Duhamel type operators play a central role in proving the main results." @default.
- W3005954743 created "2020-02-24" @default.
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- W3005954743 date "2020-07-01" @default.
- W3005954743 modified "2023-09-23" @default.
- W3005954743 title "Local and global well-posedness, and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math>-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in L" @default.
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- W3005954743 doi "https://doi.org/10.1016/j.jfa.2020.108511" @default.
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