A sharp Sobolev-Strichartz estimate for the wave equation

Maximizers for the Strichartz Inequalities and the Sobolev-strichartz Inequalities for the Schrödinger Equation

In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions based on the recent linear profile decomposition results. We then present a new proof of the linear profile decomposition for the Schröindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer ...

Characteristic Strichartz Estimates for the Wave Equation

An Inverse Theorem for the Bilinear L Strichartz Estimate for the Wave Equation

A standard bilinear L Strichartz estimate for the wave equation, which underlies the theory of X spaces of Bourgain and Klainerman-Machedon, asserts (roughly speaking) that if two finite-energy solutions to the wave equation are supported in transverse regions of the light cone in frequency space, then their product lies in spacetime L with a quantitative bound. In this paper we consider the in...

Strichartz Estimates for Wave Equations with Coefficients of Sobolev Regularity

Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. We use such methods to show that the existing results for C1,1 and C1,α coefficients can be improved when the coefficients of the wave operator lie in a Sobolev space of sufficiently high order.

A Sharp Inequality for the Strichartz Norm

Let u : R × R → C be the solution of the linear Schrödinger equation