2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218974The space-time monopole equation on $\R^{2+1}$ can be derived by a dimensional reduction of the anti-self-dual Yang Mills equations on $\R^{2+2}$. It can be also viewed as the hyperbolic analog of Bogomolny equations. We uncover null forms in the nonlinearities and employ optimal bilinear estimates in the framework of Wave-Sobolev spaces. As a result, we show the equation is locally wellposed in the Coulomb gauge for initial data sufficiently small in $H^s$ for $s>{1/4}$.23 pages; Added some remarks, and rewrote parts of Sections 4 and 5; SubmittedAnalysis of PDEs70S15; 35L70text