Low regularity well-posedness for the Yang-Mills system in 2D

Hartmut Pecher

Low regularity well-posedness for the Yang-Mills system in 2D

Analysis of PDEs 2020-10-14 v1

Authors: Hartmut Pecher

Abstract

The Cauchy problem for the Yang-Mills system in two space dimensions is treated for data with minimal regularity assumptions. In the classical case of data in $L^2$ -based Sobolev spaces we have to assume that the number of derivatives is more than $3/4$ above the critical regularity with respect to scaling. For data in $L^r$ -based Fourier-Lebesgue spaces this result can be improved by $1/4$ derivative in the sense of scaling as $r \to 1$ .

Keywords

yang-mills theory cauchy problem sobolev regularity of partial differential equations

Cite

@article{arxiv.2010.06170,
  title  = {Low regularity well-posedness for the Yang-Mills system in 2D},
  author = {Hartmut Pecher},
  journal= {arXiv preprint arXiv:2010.06170},
  year   = {2020}
}

Comments

23 pages. arXiv admin note: substantial text overlap with arXiv:1911.05537, arXiv:1703.01949; text overlap with arXiv:1408.5363 by other authors

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