Local well-posedness for the nonlinear Dirac equation in two space dimensions

Hartmut Pecher

doi:10.3934/cpaa.2014.13.673

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2014, Volume 13, Issue 2: 673-685. Doi: 10.3934/cpaa.2014.13.673

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Local well-posedness for the nonlinear Dirac equation in two space dimensions

Hartmut Pecher^1,

1.
Fachbereich Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42097 Wuppertal

Received: March 2013

Revised: August 2013

Published: March 2014

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Abstract

The Cauchy problem for the cubic nonlinear Dirac equation in two space dimensions is locally well-posed for data in $H^s$ for $ s > 1/2$. The proof given in spaces of Bourgain-Klainerman-Machedon type relies on the null structure of the nonlinearity as used by d'Ancona-Foschi-Selberg for the Dirac-Klein-Gordon system before and bilinear Strichartz type estimates for the wave equation by Selberg and Foschi-Klainerman.

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Mathematics Subject Classification: 35Q55, 35L70.

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