Title and Abstract

14th, 13:15 - 14:15

Improvement of orthonormal Strichartz estimates on tori by renormalisation

We consider orthonormal Strichartz estimates for the free Schrödinger equation on the torus. They can be viewed as space-time estimates for the density associated with the von Neumann equation. In this talk, we introduce a renormalisation of the density and study its effect. On the one-dimensional torus, we show that the renormalised density satisfies better estimates than the non-renormalized density, which was studied in Nakamura (2020, Trans. Amer. Math. Soc.). However, since we cannot prove the result for a range of exponents, we present this case as a conjecture. Finally, we also show that, on T^d with d \ge 2, any improvement by our renormalisation is small even if it occurs.

This talk is based on joint work with Andrew Rout (Politecnico di Milano).