Local wellposedness for the 2+1 dimensional monopole equation
Czubak, Magdalena
Original · EN
The space-time monopole equation on ²⁺¹ can be derived by a dimensional reduction of the anti-self-dual 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.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.