Profiles for the radial focusing energy-critical wave equation in odd\n dimensions

2014/12/03 by Casey Rodriguez, Rodriguez, Casey
Mathematics · #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1412.1388

Abstract

In this paper we consider global and non-global radial solutions of the\nfocusing energy--critical wave equation on \ℝ \× \ℝ^N\nwhere N \≥ 5 is odd. We prove that if the solution remains bounded in the\nenergy space as you approach the maximal forward time of existence, then along\na sequence of times converging to the maximal forward time of existence, the\nsolution decouples into a sum of dynamically rescaled solitons, a free\nradiation term, and an error tending to zero in the energy space. If, in\naddition, we assume a bound on the evolution that rules out formation of\nmultiple solitons, then this decoupling holds for all times approaching the\nmaximal forward time of existence.\n

Related

• Profiles for the radial focusing 4d energy-critical wave equation
• Profiles of bounded radial solutions of the focusing, energy-critical wave equation
• Soliton resolution for the radial critical wave equation in all odd space dimensions
• Decay estimates for nonradiative solutions of the energy-critical\n focusing wave equation
• Soliton resolution for the energy-critical nonlinear wave equation in the radial case