Global existence for solutions of the focusing wave equation with the compactness property (Q342607)

Initial value problems for the energy-critical wave equation in dimensions 3,4 and 5 are considered. Solutions with compactness property to this type of equations are investigated. In the present paper one shows an extension of the result on ``non-existence of self-similar solutions with the compactness property'' proved in an article of two last named authors [Acta Math. 201, No. 2, 147--212 (2008; Zbl 1183.35202)]. Actually one proves that any solution of the considered mathematical model having the compactness property is global. A similar result is proved for the energy-supercritical nonlinear Schrödinger equation.