Nonlinear Schrödinger equations with critical Hardy potential and Choquard nonlinearity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914448621436928 |
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| author | Nguyen, Phuoc-Tai Tran, Tuan Dat |
| author_facet | Nguyen, Phuoc-Tai Tran, Tuan Dat |
| contents | We study the Cauchy problem for the nonlinear Schrödinger equation characterized by contrasting effects between the concentration at the origin of a critical Hardy potential and the intrinsic nonlocality of a Choquard nonlinearity. We prove the existence of a ground state solution through optimizers of an interpolation Hardy-Gagliardo-Nirenberg inequality and derive a non-existence result via Poho\v zaev identities. Using these results, we provide various criteria for the global existence and finite-time blow-up for the problem in the energy-subcritical regime. Finally, we establish a key compactness result, which enables us to obtain a characterization of finite-time blow-up solutions with minimal mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Schrödinger equations with critical Hardy potential and Choquard nonlinearity Nguyen, Phuoc-Tai Tran, Tuan Dat Analysis of PDEs 35Q55, 35B44, 35A02, 35A15, 35Q40 We study the Cauchy problem for the nonlinear Schrödinger equation characterized by contrasting effects between the concentration at the origin of a critical Hardy potential and the intrinsic nonlocality of a Choquard nonlinearity. We prove the existence of a ground state solution through optimizers of an interpolation Hardy-Gagliardo-Nirenberg inequality and derive a non-existence result via Poho\v zaev identities. Using these results, we provide various criteria for the global existence and finite-time blow-up for the problem in the energy-subcritical regime. Finally, we establish a key compactness result, which enables us to obtain a characterization of finite-time blow-up solutions with minimal mass. |
| title | Nonlinear Schrödinger equations with critical Hardy potential and Choquard nonlinearity |
| topic | Analysis of PDEs 35Q55, 35B44, 35A02, 35A15, 35Q40 |
| url | https://arxiv.org/abs/2604.04609 |