Numerical simulations for the energy-supercritical nonlinear wave equation

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.

28 pages, 13 figures. New references and new cases added

References in corpus (7)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Scattering for the radial 3d cubic wave equation
• On the Energy Subcritical, Non-linear Wave Equation with Radial Data for $p\in (3,5)$
• Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
• The radial defocusing energy-supercritical NLS in dimension four
• The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+5}

Cited by in corpus (1)

• A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails