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Spinning Q-balls for the Klein-Gordon-Maxwell equations. (English) Zbl 1194.78009

The paper deals with the nonlinear Klein-Gordon-Maxwell equations \(\frac{\partial^2\psi}{\partial t^2} - \nabla\psi +W'(\psi)=0\), where the nonlinear term \(W\) is assumed to be positive and \(W(0)=0\). The vortices in the nonlinear Klein-Gordon equation are often considered in the Physics literature with the name of spinning \(Q\)-balls. The main result of the paper is the proof of existence of spinning \(Q\)-balls for the nonlinear Klein-Gordon-Maxwell equations, that is, three-dimensional vortex-solutions which are finite energy, stationary solutions such that the matter field has a nontrivial angular momentum and the magnetic field looks like the field created by a finite solenoid.

MSC:

78A25 Electromagnetic theory (general)
47J30 Variational methods involving nonlinear operators
35J50 Variational methods for elliptic systems
81V10 Electromagnetic interaction; quantum electrodynamics
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