Iterative methods fail to solve NLS below the Sobolev embedding threshold on the Sierpinski gasket
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910021294489600 |
|---|---|
| author | Ruiz, Patricia Alonso Staffilani, Gigliola |
| author_facet | Ruiz, Patricia Alonso Staffilani, Gigliola |
| contents | We show that the nonlinear Schrödinger equation on the Sierpinski gasket with a power nonlinearity of order $2k{+}1$ is not locally well-posed for initial data just below the regularity threshold for the Sobolev embedding $H^s\subseteq L^\infty$. More precisely, the flow map fails to be $C^{2k+1}$-continuous in any Sobolev space $H^s$ below that threshold, and the threshold is independent of the power nonlinearity. This novel behavior significantly differs from other compact spaces such as the torus or the sphere, and it is directly connected to the existence of localized eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative methods fail to solve NLS below the Sobolev embedding threshold on the Sierpinski gasket Ruiz, Patricia Alonso Staffilani, Gigliola Analysis of PDEs 58J50, 28A80 We show that the nonlinear Schrödinger equation on the Sierpinski gasket with a power nonlinearity of order $2k{+}1$ is not locally well-posed for initial data just below the regularity threshold for the Sobolev embedding $H^s\subseteq L^\infty$. More precisely, the flow map fails to be $C^{2k+1}$-continuous in any Sobolev space $H^s$ below that threshold, and the threshold is independent of the power nonlinearity. This novel behavior significantly differs from other compact spaces such as the torus or the sphere, and it is directly connected to the existence of localized eigenfunctions. |
| title | Iterative methods fail to solve NLS below the Sobolev embedding threshold on the Sierpinski gasket |
| topic | Analysis of PDEs 58J50, 28A80 |
| url | https://arxiv.org/abs/2505.04515 |