Numerical simulations for the energy-supercritical nonlinear wave equation. (8th October 2020)

• Record Type: Journal Article
• Authors: Murphy, Jason; Zhang, Yanzhi
• Is Part Of: Nonlinearity. Volume 33:Number 11(2020)
• Page Start: 6195
• Page End: 6220
• Publication Date: 2020-10-08
• Subjects: nonlinear wave equations -- energy-supercritical -- conditional scattering; nonlinear wave equations -- energy-supercritical -- conditional scattering; 35L70; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aba235
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numerically that the critical Sobolev norm of solutions remains bounded in time. This lends support to conditional scattering results that have been recently established for nonlinear wave equations.