Some Sharp Strichartz Inequalities

Explore the intricacies of sharp Strichartz inequalities in this 44-minute lecture by D. Oliveira e Silva at the Hausdorff Center for Mathematics. Delve into the connection between Strichartz estimates for the homogeneous Schrödinger equation and adjoint Fourier restriction estimates on the paraboloid. Trace the brief yet rich history of extremizers and sharp constants in these inequalities. Focus on the case of certain planar power curves, learning how a geometric comparison principle for convolution measures establishes sharp Strichartz inequality and determines the existence of extremizers. Understand the mechanism behind potential lack of compactness through the behavior of extremizing sequences, explained via concentration-compactness. Discover how this research resolves a dichotomy in recent literature regarding the existence of extremizers for the fourth-order Schrödinger equation in one spatial dimension. Gain insights from this collaborative work with Gianmarco Brocchi and René Quilodrán, expanding your knowledge of advanced mathematical concepts in Strichartz inequalities and related fields.