Endpoint estimates and global existence for the nonlinear Dirac equation with potential

Details Endpoint estimates and global existence for the nonlinear Dirac equation with potential Endpoint estimates and global existence for the nonlinear Dirac equation with potential

2011-03-21

arxiv.org/abs/1103.4014v1

Mathematics

Analysis of PDEs

Scientific paper

We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for small initial $H^{1}$ data with additional angular regularity. This implies in particular global existence in the critical energy space $H^{1}$ for small radial data.

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