Global boundedness of the curl for a p-curl system in convex domains

TL;DR

This paper investigates a semilinear curl system in convex domains related to superconductivity, establishing existence and boundedness of solutions, which advances understanding of mathematical models in physics.

Contribution

It proves the existence and $L^{ty}$ bounds of weak solutions for a semilinear curl system in convex domains, a novel result in this context.

Findings

Existence of weak solutions established.

Solutions are bounded in the $L^{ty}$ norm.

Applicable to models of superconductivity.

Abstract

In this paper, we study a semilinear system involving the curl operator in a bounded and convex domain in $R^3$, which comes from the steady-state approximation for Bean critical-state model for type-II superconductors. We show the existence and the $L^{\infty}$ estimate for weak solutions to this system.