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

Abstract

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.

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

References in corpus (2)

• Sharp estimates for maximal operators associated to the wave equation
• Dispersive Estimates for Schrödinger Operators with Measure-Valued Potentials in R^3

Cited by in corpus (11)

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• Attractors of Hamilton nonlinear partial differential equations
• Time decay estimates for the wave equation with potential in dimension two
• Multisolitons for the defocusing energy critical wave equation with potentials
• Dispersive Estimates in R^3 with Threshold Resonances
• Strichartz Estimates for Wave equations with Charge Transfer Hamiltonian
• Wave equations with moving potentials
• Strichartz estimates for the Klein--Gordon equation in ${\mathbb{R}}^{3+1}$
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• Global center stable manifold for the defocusing energy critical wave equation with potential