arXiv:1212.0568 Abstract | arXiv Analytics

arXiv:1212.0568 [math.AP]Abstract References Reviews Resources

Strichartz Estimates and Maximal Operators for the Wave Equation in R^3

Published 2012-12-03, updated 2012-12-25Version 2

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by Rogers--Villaroya, 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.

Comments: 30 pages. Updated to fix minor typos and to acknowledge previous work by D'Ancona-Pierfelice

Categories: math.AP

Subjects: 35L05, 42A85

Keywords: strichartz estimates, maximal operator estimates, sharp strichartz-type estimates, reverse spacetime norms, small initial data

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