Regularity of a Parabolic System Involving Curl

TL;DR

This paper establishes a regularity result for a linear parabolic system involving curl, with boundary conditions prescribing the tangential component, contributing to the mathematical understanding of such PDEs.

Contribution

It provides a new regularity proof for a parabolic system involving curl with specific boundary conditions, advancing theoretical PDE analysis.

Findings

Proved regularity for the parabolic system involving curl.

Established boundary condition effects on solution smoothness.

Enhanced understanding of linear parabolic PDEs with curl constraints.

Abstract

This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the boundary condition of prescribing the tangential component of the solution.