Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces

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 ± |x|^−b|u|^α−1u=0, 1<α< 5−2b and 0< b≤ 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 L̂^p spaces for 4/3<p<8. Primarily, we prove global well-posedness for arbitrarily large initial data via the data decomposition method adapted for the Fourier-Lebesgue spaces, with generalized Strichartz estimates for p<2 and classical Strichartz estimates for p>2. Furthermore, we obtain analogous results for (INLS) in modulation spaces M^p,p' for 4/3<p<2.

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BibTeX RIS

BibTeX

@misc{bhimani2026inhomogeneous,
  title = {{Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces}},
  author = {Divyang G. Bhimani and Diksha Dhingra and Vijay Kumar Sohani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.30777},
  eprint = {2608.30777},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30777},
}

RIS

TY  - UNPB
TI  - Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces
AU  - Divyang G. Bhimani
AU  - Diksha Dhingra
AU  - Vijay Kumar Sohani
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.30777
UR  - https://arxiv.org/abs/2608.30777
AB  - 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 ± |x|^−b|u|^α−1u=0, 1<α< 5−2b and 0< b≤ 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 L̂^p spaces for 4/3<p<8. Primarily, we prove global well-posedness for arbitrarily large initial data via the data decomposition method adapted for the Fourier-Lebesgue spaces, with generalized Strichartz estimates for p<2 and classical Strichartz estimates for p>2. Furthermore, we obtain analogous results for (INLS) in modulation spaces M^p,p' for 4/3<p<2.
ER  -

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