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

The space-time monopole equation on 2+1 can be derived by a dimensional reduction of the antiselfdual Yang–Mills equations on 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 Hs for s > 1 4.

monopole, null form, Coulomb gauge, wellposedness
Mathematical Subject Classification 2000
Primary: 35L70, 70S15
Received: 10 February 2009
Revised: 15 September 2009
Accepted: 21 January 2010
Published: 8 June 2010
Magdalena Czubak
Department of Mathematics
University of Toronto
40 Saint George Street
Toronto, Ontario M5S 2E4