Strichartz estimates and maximal operators for the wave equation in R3

By Marius Beceanu, M. Goldberg. 2012

54 citations recorded by the source corpus.

Abstract We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse space–time norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by Rogers–Villarroya, of which we prove a sharper version. As a sample application, we use these results to prove the local well-posedness and the global well-posedness for small initial data of semilinear wave equations in R 3 with quintic or higher monomial nonlinearities.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68a123b10f72fa6ae20660da681c898d84cb8986

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In Applied Mathematics

1. M. Goldberg
2. William R. Green

In Mathematical Physics

1. William R. Green
2. M. Goldberg

Citations in the corpus

• Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy (2013, background): “The bulk of the results are in three dimensions, we note for example [3, 4, 6, 9, 10, 16].”