Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917114621722624 |
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| author | Ardila, Alex H. Murphy, Jason Zheng, Jiqiang |
| author_facet | Ardila, Alex H. Murphy, Jason Zheng, Jiqiang |
| contents | We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+Δ)u = |u|^2 u - |u|^4 u. \] In [18, 23], the authors classified the dynamics of solutions under the energy constraint $E(u)< E^c(W)$, where $W$ is the quintic NLS ground state and $E^c$ is the quintic NLS energy. In this work we classify the dynamics of $H^1$ solutions at the threshold $E(u)=E^c(W)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13531 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity Ardila, Alex H. Murphy, Jason Zheng, Jiqiang Analysis of PDEs We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+Δ)u = |u|^2 u - |u|^4 u. \] In [18, 23], the authors classified the dynamics of solutions under the energy constraint $E(u)< E^c(W)$, where $W$ is the quintic NLS ground state and $E^c$ is the quintic NLS energy. In this work we classify the dynamics of $H^1$ solutions at the threshold $E(u)=E^c(W)$. |
| title | Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.13531 |