Skip to content
DraconiticResearch
Search Sources API
181,686 studies31 sourcesUpdated 19 min ago
PreprintCC BY 4.0arXiv

Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential

  • Tiesong Jiang
  • Kexue Li
Open at sourcePDFDOICite

Abstract

We prove dispersive estimates for the three-dimensional defocusing energy-critical nonlinear Schrödinger equation associated with ℒa=−Δ+a|x|−2. For nonnegative potentials, we extend the known finite-p theory to the endpoint L1→ L∞. For negative potentials in the global well-posedness range, set σ=1/2−√(1/4+a). We obtain the free strong decay rate for 2<p<3/σ and the limiting Lorentz estimate from L(3/σ)',1 to L3/σ,∞. The restriction p<3/σ is sharp for strong Lebesgue decay. The proof combines a finite-interval bootstrap, nonlinear real interpolation on bounded energy sets, and endpoint Sobolev--Lorentz estimates adapted to ℒa.

Related

  1. Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential
    Xitao Gao, Qiuye Jia, Junyong Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  2. Dispersive decay for the Nonlinear magnetic Schrödinger equation
    Lei Wei, Zhi Wenduan
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Dispersive and Strichartz Estimates for the Schrödinger Equation Inside Cylindrical Domains
    Len Meas
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  4. Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds
    Baiyang Yin, Fang Zhang, Junyong Zhang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. On 2D Scattering for a Critical Nonlinear Schrödinger Flow
    Vladimir Georgiev, Tohru Ozawa
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{jiang2026strong,
  title = {{Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential}},
  author = {Tiesong Jiang and Kexue Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07585},
  eprint = {2609.07585},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07585},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential
AU  - Tiesong Jiang
AU  - Kexue Li
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07585
UR  - https://arxiv.org/abs/2609.07585
AB  - We prove dispersive estimates for the three-dimensional defocusing energy-critical nonlinear Schrödinger equation associated with ℒ_a=−Δ+a|x|^−2. For nonnegative potentials, we extend the known finite-p theory to the endpoint L^1→ L^∞. For negative potentials in the global well-posedness range, set σ=1/2−√(1/4+a). We obtain the free strong decay rate for 2<p<3/σ and the limiting Lorentz estimate from L^(3/σ)',1 to L^3/σ,∞. The restriction p<3/σ is sharp for strong Lebesgue decay. The proof combines a finite-interval bootstrap, nonlinear real interpolation on bounded energy sets, and endpoint Sobolev--Lorentz estimates adapted to ℒ_a.
ER  -