Higher regularity of the "tangential" fields in the relativistic Vlasov-Maxwell system

TL;DR

This paper proves that the tangential electric and magnetic fields in the relativistic Vlasov-Maxwell system are more regular than previously known, being bounded in a specific Lebesgue space with a small positive exponent.

Contribution

It establishes higher regularity of the tangential fields in the relativistic Vlasov-Maxwell system, improving understanding of their boundedness properties.

Findings

Tangential fields are bounded in $L^ abla_{loc,t} L^{2+ abla}_x$ for some $ abla>0$

Enhanced regularity results for the fields in the system

Improved bounds in the Glassey-Strauss representation formulas

Abstract

It is shown that the "tangential" electric and magnetic fields, in the Glassey-Strauss representation formulas, are in fact bounded in $L^\infty_{{\rm loc},\,t} L^{2+\delta}_x$ for some $\delta>0$.