On Strichartz Estimates
Jørgen de Battista Kvamme, Master student @ Department of Mathematics, UiB
Abstract
In this seminar, we start by introducing the Linear Schrödinger Equation, a differential equation widely used in physics. In order to bound the space-time norm of the solution, with the norm of the initial data, we study a specific set of estimates called Strichartz estimates. In these estimates we take the L^q norm in time and L^r norm in space. The dimension n together with r,q must satisfy a specific inequality. For n>2 it was a long standing problem, whether this set of estimates still holds when they attain equality in the given inequality.
In 1998, Markus Keel and Terrence Tao, published a paper on this problem, proving that the endpoint Strichartz estimate holds for an even more general set of operators, satisfying some specific conditions. The main concern of this talk will be to go through this paper from Keel and Tao, and lay out the heart of the proof