TY - JOUR
T1 - Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in Lp-based Sobolev spaces
AU - Dodson, Benjamin
AU - Soffer, Avraham
AU - Spencer, Thomas
N1 - Funding Information: The authors thank J. Bourgain, P. Deift, J. Lebowitz, and W. Schlag for helpful discussions. B.D. gratefully acknowledges the support of NSF Grant Nos. DMS-1500424 and DMS-1764358. He also gratefully acknowledges support from the von Neumann Fellowship at the Institute for Advanced Study. A.S. was supported, in part, by NSF Grant No. DMS-160074. Publisher Copyright: © 2021 Author(s).
PY - 2021/7/1
Y1 - 2021/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85111663120&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85111663120&partnerID=8YFLogxK
U2 - https://doi.org/10.1063/5.0042321
DO - https://doi.org/10.1063/5.0042321
M3 - Article
SN - 0022-2488
VL - 62
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 7
M1 - 071507
ER -