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arXiv · 2608.30777

Inhomogeneous nonlinear Schr\"odinger equation in Fourier-Lebesgue and modulation spaces

Divyang G. Bhimani·Diksha Dhingra·Vijay Kumar Sohani
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Abstract

The purpose of this work is to provide a broader framework for analyzing the inhomogeneous nonlinear Schr\"odinger equation (INLS) \[iu_t + u_{xx} \pm |x|^{-b}|u|^{\alpha-1}u=0, \quad 1<\alpha< 5-2b\; \text{and}\; 0< b\leq 1/4.\] Specifically, we establish low-regularity well-posedness in the Fourier-Lebesgue $\widehat{L}^{p}$ spaces for $4/3 2$. Primarily, in both cases, we prove global well-posedness for arbitrarily large initial data via the data decomposition method adapted for the Fourier-Lebesgue spaces. Furthermore, we obtain analogous results for INLS in modulation spaces $M^{p,p'}$ for $4/3<p<2$.

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Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani. 2026-08-31. Inhomogeneous nonlinear Schr\"odinger equation in Fourier-Lebesgue and modulation spaces. https://arxiv.org/abs/2608.30777

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