Endpoint estimates and global existence for the nonlinear Dirac equation with potential. (English) Zbl 1260.35159
Summary: 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.
MSC:
35Q41 | Time-dependent Schrödinger equations and Dirac equations |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |