Forward self-similar solutions to the viscoelastic Navier-Stokes equation with damping

TL;DR

This paper proves the existence of smooth, global, forward self-similar solutions to the viscoelastic Navier-Stokes equations with damping, for initial data homogeneous of degree -1, extending understanding of such fluid models.

Contribution

It establishes the existence of global, smooth, self-similar solutions for a viscoelastic fluid model with damping, for a broad class of initial data.

Findings

Existence of global, smooth, forward self-similar solutions.

Solutions are valid for initial data homogeneous of degree -1.

Extends previous results to viscoelastic Navier-Stokes with damping.

Abstract

Motivated by \cite{JS}, we prove that there exists a global, forward self-similar solution to the viscoelastic Navier-Stokes equation with damping, that is smooth for $t>0$, for any initial data that is homogeneous of degree $-1$.