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arXiv · 2604.00252

Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle

Sonae Hadama·Andrew Rout
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Abstract

In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schr\"odinger 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). 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 $d \ge 2$ is minimal.

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Sonae Hadama, Andrew Rout. 2026-03-31. Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle. https://arxiv.org/abs/2604.00252

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