Strichartz and dispersive estimates for quantum bouncing ball model: exponential sums and Van der Corput methods in 1d semi-classical Schrödinger equations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908573342105600 |
|---|---|
| author | Ivanovici, Oana |
| author_facet | Ivanovici, Oana |
| contents | We analyze the one-dimensional semi-classical Schrödinger equation on the half-line with a linear potential and Dirichlet boundary conditions. Our main focus is on establishing improved dispersive and Strichartz estimates for this model, which govern the space-time behavior of solutions. We prove refined Strichartz bounds using Van der Corput-type derivative tests, beating previous known results where Strichartz estimates incur 1/4 losses. Moreover, assuming sharp bounds for certain exponential sums, our results indicate the possibility to reduce these losses further to $1/6 + ε$ for all $ε>0$, which would be sharp. We further expect that analogous Strichartz bounds should hold within the Friedlander model domain in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz and dispersive estimates for quantum bouncing ball model: exponential sums and Van der Corput methods in 1d semi-classical Schrödinger equations Ivanovici, Oana Analysis of PDEs Number Theory We analyze the one-dimensional semi-classical Schrödinger equation on the half-line with a linear potential and Dirichlet boundary conditions. Our main focus is on establishing improved dispersive and Strichartz estimates for this model, which govern the space-time behavior of solutions. We prove refined Strichartz bounds using Van der Corput-type derivative tests, beating previous known results where Strichartz estimates incur 1/4 losses. Moreover, assuming sharp bounds for certain exponential sums, our results indicate the possibility to reduce these losses further to $1/6 + ε$ for all $ε>0$, which would be sharp. We further expect that analogous Strichartz bounds should hold within the Friedlander model domain in higher dimensions. |
| title | Strichartz and dispersive estimates for quantum bouncing ball model: exponential sums and Van der Corput methods in 1d semi-classical Schrödinger equations |
| topic | Analysis of PDEs Number Theory |
| url | https://arxiv.org/abs/2510.01779 |