University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Strichartz estimates for the wave equation on flat cones and applications

Strichartz estimates for the wave equation on flat cones and applications

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With Matt Blair and G. Austin Ford, we consider the solution operator for the wave equation on the flat Euclidean cone. Using explicit representations of the solution operator in regions related to flat wave propagation and diffraction by the cone point, we prove dispersive estimates and hence scale invariant Strichartz estimates for the wave equation on flat cones. We then show that this yields corresponding inequalities on wedge domains, polygons, and Euclidean surfaces with conic singularities. This in turn yields well-posedness results for the nonlinear wave equation on such manifolds. Morawetz estimates on the cone are also treated.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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