Local well-posedness for the space-time Monopole equation in Lorenz gauge

Nikolaos Bournaveas; Timothy Candy

doi:10.1007/s00030-011-0118-1

Local well-posedness for the space-time Monopole equation in Lorenz gauge

Analysis of PDEs 2011-10-31 v1

Authors: Nikolaos Bournaveas , Timothy Candy

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Abstract

It is known from the work of Czubak that the space-time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in $H^s(\mathbb{R}^2)$ for $s>1/4$ . Here we prove local well-posedness for arbitrary initial data in $H^s(\mathbb{R^2})$ with $s>1/4$ in the Lorenz gauge.

Keywords

space-time Monopole equation local well-posedness Lorenz gauge Coulomb gauge initial data Sobolev space partial differential equations

Cite

@article{arxiv.1110.6342,
  title  = {Local well-posedness for the space-time Monopole equation in Lorenz gauge},
  author = {Nikolaos Bournaveas and Timothy Candy},
  journal= {arXiv preprint arXiv:1110.6342},
  year   = {2011}
}

Comments

To appear in NoDEA

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