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arXiv · 2203.09614

Soliton resolution for the energy-critical nonlinear wave equation in the radial case

Jacek Jendrej·Andrew Lawrie
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Abstract

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \ge 4$. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution $W$, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.

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Jacek Jendrej, Andrew Lawrie. 2022-03-17. Soliton resolution for the energy-critical nonlinear wave equation in the radial case. https://arxiv.org/abs/2203.09614

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