Generation Of Decay Estimates And Application To Scattering Of Rough Solutions Of 3D NLKG

Details Generation Of Decay Estimates And Application To Scattering Of Rough Solutions Of 3D NLKG Generation Of Decay Estimates And Application To Scattering Of Rough Solutions Of 3D NLKG

2010-07-31

arxiv.org/abs/1008.0094v1

Mathematics

Analysis of PDEs

41 pages

Scientific paper

We prove scattering of solutions just below the energy norm of the 3D Klein-Gordon equation: this result extends those obtained in the energy class and those obtained below the energy norm under the additional assumption of spherical symmetry. It is well-known that the notion of scattering is closely related to that of decay. The main difficuly is that, unlike the radial case, there is no useful decay estimate available. The idea is to generate some decay estimates, by means of concentration and a low-high frequency decomposition.

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