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The Energy Critical Wave Equation in 3D

The Energy Critical Wave Equation in 3D

(p.215) Chapter Nine The Energy Critical Wave Equation in 3D
Advances in Analysis
Carlos Kenig, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Princeton University Press

This chapter discusses the energy critical nonlinear wave equation in 3 space dimensions. It mainly focuses on soliton resolution for radial solutions of nonlinear waves. For a long time there has been a widespread belief that global in time solutions of dispersive equations, asymptotically in time, decouple into a sum of finitely many modulated solitons, a free radiation term, and a term that goes to 0 at infinity. Such a result should hold for globally well-posed equations, or in general, with the additional condition that the solution does not blow-up. When blow-up may occur such decompositions are always expected to be unstable.

Keywords:   energy critical wave equation, energy critical nonlinear wave equation, 3D, soliton resolution, solitons

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