Differential and Integral Equations

Morawetz-Strichartz estimates for spherically symmetric solutions to wave equations and applications to semilinear Cauchy problems

Kunio Hidano

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Abstract

We prove some space-time estimates with homogeneous weight functions for the wave equation with radially symmetric data in order to explain a connection between the Morawetz-type space-time estimate and the Strichartz-type space-time estimate. As an application of such linear estimates, we give a new proof of global existence of small radial solutions to semilinear wave equations. Local existence of radial solutions is also studied for low-regularity data.

Article information

Source
Differential Integral Equations Volume 20, Number 7 (2007), 735-754.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039407

Mathematical Reviews number (MathSciNet)
MR2333654

Zentralblatt MATH identifier
1212.35036

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions

Citation

Hidano, Kunio. Morawetz-Strichartz estimates for spherically symmetric solutions to wave equations and applications to semilinear Cauchy problems. Differential Integral Equations 20 (2007), no. 7, 735--754. https://projecteuclid.org/euclid.die/1356039407.


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