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2010 Local wellposedness for the 2+1-dimensional monopole equation
Magdalena Czubak
Anal. PDE 3(2): 151-174 (2010). DOI: 10.2140/apde.2010.3.151

Abstract

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>14.

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Magdalena Czubak. "Local wellposedness for the 2+1-dimensional monopole equation." Anal. PDE 3 (2) 151 - 174, 2010. https://doi.org/10.2140/apde.2010.3.151

Information

Received: 10 February 2009; Revised: 15 September 2009; Accepted: 21 January 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1227.35211
MathSciNet: MR2657452
Digital Object Identifier: 10.2140/apde.2010.3.151

Subjects:
Primary: 35L70, 70S15

Rights: Copyright © 2010 Mathematical Sciences Publishers

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