Scattering for the $2d$ NLS with inhomogeneous nonlinearities
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914197133066240 |
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| author | Baker, Luke |
| author_facet | Baker, Luke |
| contents | We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schrödinger equations in two space dimensions for all powers $p>0$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case $0<p\leq 2$. We use the method of concentration-compactness and contradiction. We preclude the existence of compact solutions using a Morawetz estimate in the style of Nakanishi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scattering for the $2d$ NLS with inhomogeneous nonlinearities Baker, Luke Analysis of PDEs We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schrödinger equations in two space dimensions for all powers $p>0$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case $0<p\leq 2$. We use the method of concentration-compactness and contradiction. We preclude the existence of compact solutions using a Morawetz estimate in the style of Nakanishi. |
| title | Scattering for the $2d$ NLS with inhomogeneous nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.11205 |