2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60757We prove that the Maxwell-Klein-Gordon equations on $\R^{1+4}$ relative to the Coulomb gauge are locally well-posed for initial data in $H^{1+ε}$ for all $ε> 0$. This builds on previous work by Klainerman and Machedon who proved the corresponding result for a model problem derived from the Maxwell-Klein-Gordon system by ignoring the elliptic features of the system, as well as cubic terms.Analysis of PDEs35Q40; 35L70text