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VOL. 85 | 2020 Weighted $L^2-L^2$ estimate for wave equation in $\mathbf{R}^3$ and its applications
Ning-An Lai

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

In this work we establish a weighted $L^2 - L^2$ estimate for inhomogeneous wave equation in 3-D, by introducing a Morawetz multiplier with weight to the power $s(1 \lt s \lt 2)$, and then integrating on the light cones and $t$ slice. With this weighted $L^2 - L^2$ estimate in hand, we may give a new proof of global existence for small data Cauchy problem of semilinear wave equation with supercritical power in 3-D. What is more, by combining the Huygens' principle for wave equations in 3-D, the global existence for semilinear wave equation with scale invariant damping in 3-D is established.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510269

Subjects:
Primary: 35B44, 35L71

Rights: Copyright © 2020 Mathematical Society of Japan

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