Energy-critical inhomogeneous nonlinear Schrödinger equation with two power-type nonlinearities
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910868691746816 |
|---|---|
| author | Gomes, Andressa Cardoso, Mykael |
| author_facet | Gomes, Andressa Cardoso, Mykael |
| contents | We consider the initial value problem for the inhomogeneous nonlinear Schrödinger equation with double nonlinearities (DINLS)
\begin{equation*}
i \partial_t u + Δu = λ_1 |x|^{-b_1}|u|^{p_1}u + λ_2|x|^{-b_2}|u|^{\frac{4-2b_2}{N-2}}u,
\end{equation*} where $λ_1,λ_2\in \mathbb{R}$, $3\leq N<6$ and $0<b_1,b_2<\min\{2,\frac{6-N}{2}\}$. In this paper, we establish global well-posedness results for certain parameter regimes and prove finite-time blow-up phenomena under specific conditions. Our analysis relies on stability theory, energy estimates, and virial identities adapted to the DINLS model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy-critical inhomogeneous nonlinear Schrödinger equation with two power-type nonlinearities Gomes, Andressa Cardoso, Mykael Analysis of PDEs We consider the initial value problem for the inhomogeneous nonlinear Schrödinger equation with double nonlinearities (DINLS) \begin{equation*} i \partial_t u + Δu = λ_1 |x|^{-b_1}|u|^{p_1}u + λ_2|x|^{-b_2}|u|^{\frac{4-2b_2}{N-2}}u, \end{equation*} where $λ_1,λ_2\in \mathbb{R}$, $3\leq N<6$ and $0<b_1,b_2<\min\{2,\frac{6-N}{2}\}$. In this paper, we establish global well-posedness results for certain parameter regimes and prove finite-time blow-up phenomena under specific conditions. Our analysis relies on stability theory, energy estimates, and virial identities adapted to the DINLS model. |
| title | Energy-critical inhomogeneous nonlinear Schrödinger equation with two power-type nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.10866 |