On the 3D steady flow of a second grade fluid past an obstacle

TL;DR

This paper investigates the steady three-dimensional flow of a second grade fluid around an obstacle, establishing the existence of solutions with specific decay properties and characterizing the wake region behind the obstacle.

Contribution

It proves the existence of solutions in weighted Lebesgue spaces for 3D second grade fluid flow past an obstacle, including the wake region, using advanced mathematical tools.

Findings

Existence of solutions with decay properties similar to the Oseen fundamental solution.

Characterization of the wake region behind the obstacle.

Application of fundamental Oseen tensor properties and transport equations.

Abstract

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in \cite{Koch} and properties of solutions to steady transport equation to get up to arbitrarily small $\ep$ the same decay as the Oseen fundamental solution.