Hartmut Pecher
Published 2020-10-12Version 1
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 $r \to 1$ .
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
Low regularity well-posedness for the Yang-Mills system in Fourier-Lebesgue spaces
Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension
Low regularity well-posedness for the one-dimensional Dirac - Klein - Gordon system
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