Global well-posedness of the Chern-Simons-Higgs equations with finite energy

Sigmund Selberg; Achenef Tesfahun

doi:10.3934/dcds.2013.33.2531

Article Contents

2013, Volume 33, Issue 6: 2531-2546. Doi: 10.3934/dcds.2013.33.2531

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Global well-posedness of the Chern-Simons-Higgs equations with finite energy

Sigmund Selberg^1, and
Achenef Tesfahun^1,

1.
Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim

Received: December 31, 2011

Revised: March 31, 2012

Published: June 2013

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Abstract

We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global well-posedness for more regular data. Moreover, we prove local well-posedness even below the energy regularity, using the the null structure of the system in Lorenz gauge and bilinear space-time estimates for wave-Sobolev norms.

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Mathematics Subject Classification: Primary: 35L70, 35Q40.

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References

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