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The space-time monopole equation on $\R^{2+1}$ can be derived by adimensional 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. Weuncover null forms in the nonlinearities and employ optimal bilinear estimatesin the framework of Wave-Sobolev spaces. As a result, we show the equation islocally wellposed in the Coulomb gauge for initial data sufficiently small in$H^s$ for $s>{1/4}$.

Local wellposedness for the 2+1 dimensional monopole equation