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 Lp for any 2 < p < ∞, provided that the initial data are sufficiently smooth. We do not use the complete integrability of the cubic NLS.
Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in Lp-based Sobolev spaces
Note: This paper is part of the Special Issue on Celebrating the work of Jean Bourgain.
Benjamin Dodson, Avraham Soffer, Thomas Spencer; Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in Lp-based Sobolev spaces. J. Math. Phys. 1 July 2021; 62 (7): 071507. https://doi.org/10.1063/5.0042321
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