Local wellposedness for the 2+1 dimensional monopole equation

2007/12/10 by Magdalena Czubak, Czubak, Magdalena
Mathematics · #35L70 #70S15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L70 #msc:70S15

paper · pdf · doi:10.48550/arxiv.0712.1393

23 pages; Added some remarks, and rewrote parts of Sections 4 and 5; Submitted

arxiv created 2009/02/10 · arxiv updated 2009/12/01

Abstract

The space-time monopole equation on \R²⁺¹ can be derived by a dimensional reduction of the anti-self-dual Yang Mills equations on \R²⁺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.

Related

• On the space-time Monopole equation
• Local well-posedness for the (n+1)-dimensional Maxwell-Klein-Gordon equations in temporal gauge
• Almost critical local well-posedness for the space-time Monopole equation in Lorenz gauge
• Low regularity solutions for the (2+1) - dimensional\n Maxwell-Klein-Gordon equations in temporal gauge
• Local well-posedness for the (n+1)-dimensional Yang-Mills and\n Yang-Mills-Higgs system in temporal gauge