Numerical Simulations for the Energy-Supercritical Nonlinear Wave Equation
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.
J. Murphy and Y. Zhang, "Numerical Simulations for the Energy-Supercritical Nonlinear Wave Equation," Nonlinearity, vol. 33, no. 11, pp. 6195 - 6220, IOP Publishing, Nov 2020.
The definitive version is available at https://doi.org/10.1088/1361-6544/aba235
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Conditional scattering; Energy-supercritical; Nonlinear wave equations
International Standard Serial Number (ISSN)
Article - Journal
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01 Nov 2020