Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field

Global Well-posedness for the Maxwell-klein Gordon

We prove that the critical Maxwell-Klein Gordon equation on R is globally well-posed for smooth initial data which are small in the energy. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.

Non-relativistic limit of Klein-Gordon Maxwell

We deal with the derivation of the Schrödinger-Poisson system as a non-relativistic limit (i.e. c→∞ where c is the speed of light) of the Klein-GordonMaxwell or the Dirac-Maxwell system on R. We deal with convergence in the energy space C([0, T ];H). We use and motivate a splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to elect...

Concentration Compactness for the Critical Maxwell-klein-gordon Equation

We prove global regularity, scattering and a priori bounds for the energy critical MaxwellKlein-Gordon equation relative to the Coulomb gauge on (1 + 4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gérard profile decomposition [1] and a concentration compactness/rigidity argument by Kenig-Merle [5], following the method developed by the first author and Schlag [10] in...

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas.

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, ...

Nonrelativistic limit of Klein-Gordon-Maxwell to Schrödinger-Poisson