Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations

Thomas Duyckaerts; Carlos E. Kenig; Frank Merle

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arXiv · 1311.0665

Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations

Thomas Duyckaerts·Carlos E. Kenig·Frank Merle

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Abstract

Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space translation, to a sum of solitary waves. This result is a consequence of a new general compactness/rigidity argument based on profile decomposition. We also give an application of this method to the energy-critical Schrödinger equation.

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Thomas Duyckaerts, Carlos E. Kenig, Frank Merle. 2014-03-21. Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. https://arxiv.org/abs/1311.0665

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