#### Vol. 3, No. 2, 2010

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Local wellposedness for the 2+1-dimensional monopole equation

### Magdalena Czubak

Vol. 3 (2010), No. 2, 151–174
##### Abstract

The space-time monopole equation on ${ℝ}^{2+1}$ can be derived by a dimensional reduction of the antiselfdual 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 $s>\frac{1}{4}$.

##### Keywords
monopole, null form, Coulomb gauge, wellposedness
##### Mathematical Subject Classification 2000
Primary: 35L70, 70S15