Analyticity and Gevrey-class regularity for the second-grade fluid equations

TL;DR

This paper investigates the long-term analyticity and Gevrey-class regularity of solutions to second-grade fluid equations, providing explicit bounds on the radius of analyticity that persist over time, with applications to damped Euler equations.

Contribution

It introduces a new explicit lower bound on the radius of analyticity for second-grade fluid solutions that remains positive as time approaches infinity.

Findings

Explicit lower bound on the radius of analyticity that does not vanish over time

Persistence of Gevrey-class regularity for second-grade fluid equations

Applications to damped Euler equations demonstrated

Abstract

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions to the second-grade fluid equations that does not vanish as $t\to \infty$. Applications to the damped Euler equations are given.