Global existence for semilinear wave equations with scaling invariant damping in 3-D. (September 2021)

• Record Type: Journal Article
• Authors: Lai, Ning-An; Zhou, Yi
• Is Part Of: Nonlinear analysis. Volume 210(2021)
• Publication Date: 2021-09
• Subjects: 35L71 -- 35L05 -- 35B40; Semilinear wave equation -- Scaling invariant damping -- Global existence -- Weighted L2−L2 estimate; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112392
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Global existence for small data Cauchy problem of semilinear wave equations with scaling invariant damping in 3-D is established in this work, assuming that the data are radial and the constant in front of the damping belongs to [ 1 . 5, 2 ) . The proof is based on a weighted L 2 − L 2 estimate for inhomogeneous wave equation, which is established by interpolating between energy estimate and a Morawetz type estimate.