Year: 2026
Type: preprint
Abstract: The purpose of this work is to provide a broader framework for analyzing the 1D mass-subcritical inhomogeneous nonlinear Schrödinger equation (INLS) \[iu_t + u_{xx} \pm |x|^{-b}|u|^{α-1}u=0, \quad 1<α< 5-2b\; \text{and}\; 0< b\leq 1/4.\] in Sobolev spaces of negative order, reaching almost critical Sobolev spaces by working in Fourier-Lebesgue and modulation spaces. More precisely, we establish low-regularity well-posedness in the Fourier-Lebesgue $\widehat{L}^{p}$ spaces for $4/32$. Furthermore, we obtain analogous results for (INLS) in modulation spaces $M^{p,p'}$ for $4/3
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204892071