Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle
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| Format: | Preprint |
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2026
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| _version_ | 1866912993570193408 |
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| author | Hadama, Sonae Rout, Andrew |
| author_facet | Hadama, Sonae Rout, Andrew |
| contents | In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schrödinger equations (NLSS) on a circle. We show that this renormalised density satisfies better orthonormal Strichartz estimates than the non-renormalised density, which was considered in Nakamura (2020). We leave as a conjecture the optimal range of exponents for these Strichartz estimates. As an application, we determine the critical Schatten exponent below which the cubic renormalised NLSS on the circle is globally well-posed and above which it is ill-posed. Finally, we show that the improvement for orthonormal Strichartz estimates satisfied by the renormalised density on $\mathbb{T}^d$ for $d \geq 2$ is minimal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle Hadama, Sonae Rout, Andrew Analysis of PDEs Mathematical Physics 42B37 (Primary) 35Q55, 35B45 (Secondary) In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schrödinger equations (NLSS) on a circle. We show that this renormalised density satisfies better orthonormal Strichartz estimates than the non-renormalised density, which was considered in Nakamura (2020). We leave as a conjecture the optimal range of exponents for these Strichartz estimates. As an application, we determine the critical Schatten exponent below which the cubic renormalised NLSS on the circle is globally well-posed and above which it is ill-posed. Finally, we show that the improvement for orthonormal Strichartz estimates satisfied by the renormalised density on $\mathbb{T}^d$ for $d \geq 2$ is minimal. |
| title | Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle |
| topic | Analysis of PDEs Mathematical Physics 42B37 (Primary) 35Q55, 35B45 (Secondary) |
| url | https://arxiv.org/abs/2604.00252 |