Critical local well-posedness of the nonlinear Schrödinger equation on the torus
Year: 2024
Type: article
Abstract: In this paper, we study the local well-posedness of nonlinear Schrödinger equations on tori \mathbb{T}^{d} at the critical regularity. We focus on cases where the nonlinearity |u|^{a}u is nonalgebraic with small a>0 . We prove the local well-posedness for a wide range covering the mass-supercritical regime. Moreover, we supplementarily investigate the regularity of the solution map. In pursuit of lowering a , we prove a bilinear estimate for the Schrödinger operator on tori \mathbb{T}^{d} , which enhances previously known multilinear estimates. We design a function space adapted to the new bilinear estimate and a package of Strichartz estimates, which is not based on conventional atomic spaces.
DOI: 10.4171/aihpc/137
Authors: Beomjong Kwak, Soonsik Kwon
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $700
OpenAlex ID: W4401655802