Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in Lp-based Sobolev spaces

Benjamin Dodson; Avraham Soffer; Thomas Spencer

doi:10.1063/5.0042321

Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L^p-based Sobolev spaces

Benjamin Dodson, Avraham Soffer, Thomas Spencer

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we continue our study [B. Dodson, A. Soffer, and T. Spencer, J. Stat. Phys. 180, 910 (2020)] of the nonlinear Schrödinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on was proved for real analytic data. Here, we prove global well-posedness for the 1D NLS with initial data lying in L^p for any 2 < p < ∞, provided that the initial data are sufficiently smooth. We do not use the complete integrability of the cubic NLS.

Original language	English (US)
Article number	071507
Journal	Journal of Mathematical Physics
Volume	62
Issue number	7
DOIs	https://doi.org/10.1063/5.0042321
State	Published - Jul 1 2021

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/5.0042321

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abstract = "In this paper, we continue our study [B. Dodson, A. Soffer, and T. Spencer, J. Stat. Phys. 180, 910 (2020)] of the nonlinear Schr{\"o}dinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on was proved for real analytic data. Here, we prove global well-posedness for the 1D NLS with initial data lying in Lp for any 2 < p < ∞, provided that the initial data are sufficiently smooth. We do not use the complete integrability of the cubic NLS.",

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Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L^p-based Sobolev spaces

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