## On the energy subcritical, nonlinear wave equation in $$\mathbb{R}^3$$ with radial data.(English)Zbl 1295.35330

Summary: In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical Sobolev space is globally defined in time and scatters. The proof depends on the compactness/rigidity argument, decay estimates for radial, “compact” solutions, gain of regularity arguments and the “channel of energy” method.

### MSC:

 35L71 Second-order semilinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations
Full Text:

### References:

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.