2025/03/11 by Wang, Xing, Zhang, An, Zhang, Cheng · 3 citations
#35B45 #58J40 #58J45 #58J50 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2503.08504
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schrödinger equations. Our results generalize the classical (single-function) Strichartz estimates on compact manifolds by Kapitanski, Burq-Gérard-Tzvetkov, Dinh, and extend the Euclidean orthonormal version by Frank-Lewin-Lieb-Seiringer, Frank-Sabin, Bez-Lee-Nakamura. On the flat torus, our new results for the Schrödinger equation cover prior work of Nakamura, which exploits the dispersive estimate of Kenig-Ponce-Vega. We achieve sharp results on compact manifolds by combining the frequency localized dispersive estimates for small time intervals with the duality principle due to Frank-Sabin. We construct examples to show these results can be saturated on the sphere, and we can improve them on the flat torus by using Bourgain-Demeter's decoupling theorem to obtain new decoupling inequalities for certain non-smooth hypersurfaces. As an application, we obtain the well-posedness of infinite systems of dispersive equations with Hartree-type nonlinearity.