PreprintarXiv licencearXiv
Dispersive decay for the Nonlinear magnetic Schrödinger equation
Abstract
In this paper, we obtain the dispersive estimates and global well-posedness of the nonlinear magnetic Schrödinger equation in ℝ3 with nonlinearity |u|p−1u with exponent 5/3< p<5 when the initial value stays in a suitable space Σs. By proving the resolvent estimates with weight functions and the \textquotedblleft almost equivalence\textquotedblright between (−ΔA)s/2 and (−Δ)s/2, we obtain the Strichartz estimates of |JA(t)|su:=ei|x|2/4t(−t2ΔA)s/2e(−i|x|2)/4tu, therefore the dispersive decay estimates are obtained.
Related
- Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential
- Global flows for the cubic nonlinear Schrödinger equation without decay assumptions
- Multi-peak solutions for a magnetic nonlinear Schrödinger equation with exponential critical growth in ℝ2
- Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential
- Dispersive and Strichartz Estimates for the Schrödinger Equation Inside Cylindrical Domains
BibTeX
@misc{wei2026dispersive,
title = {{Dispersive decay for the Nonlinear magnetic Schrödinger equation}},
author = {Lei Wei and Zhi Wenduan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.26756},
eprint = {2608.26756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26756},
}
RIS
TY - UNPB
TI - Dispersive decay for the Nonlinear magnetic Schrödinger equation
AU - Lei Wei
AU - Zhi Wenduan
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.26756
UR - https://arxiv.org/abs/2608.26756
AB - In this paper, we obtain the dispersive estimates and global well-posedness of the nonlinear magnetic Schrödinger equation in ℝ^3 with nonlinearity |u|^p−1u with exponent 5/3< p<5 when the initial value stays in a suitable space Σ_s. By proving the resolvent estimates with weight functions and the \textquotedblleft almost equivalence\textquotedblright between (−Δ_A)^s/2 and (−Δ)^s/2, we obtain the Strichartz estimates of |J_A(t)|^su:=e^i|x|^2/4t(−t^2Δ_A)^s/2e^(−i|x|^2)/4tu, therefore the dispersive decay estimates are obtained.
ER -