Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

TL;DR

This paper establishes the well-posedness of boundary layer equations for high Weissenberg and Reynolds number flows of non-Newtonian fluids, using a Lagrangian transformation to handle boundary conditions.

Contribution

It derives and proves the well-posedness of boundary layer equations for non-Newtonian fluids in a high Weissenberg and Reynolds number regime, with a novel Lagrangian coordinate approach.

Findings

Proved well-posedness of boundary layer equations for non-Newtonian fluids.

Derived boundary layer equations in the high Weissenberg and Reynolds number limit.

Used Lagrangian coordinates to handle boundary conditions effectively.

Abstract

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument.