Preservation of log-H\"{o}lder coefficients of the vorticity in the transport equation

TL;DR

This paper proves that the log-Hölder coefficients of solutions to the transport equation remain unchanged over time, highlighting a key regularity property of such solutions.

Contribution

The work establishes the preservation of log-Hölder coefficients in the transport equation, a novel regularity result not previously demonstrated.

Findings

Log-Hölder coefficients are preserved in time for solutions.

Provides a new regularity property for the transport equation.

Enhances understanding of solution stability over time.

Abstract

We show that the log-H\"{o}lder coefficients of a solution to the transport equation is preserved in time.