A brief functional investigation via Sobolev spaces to analyze the behavior of Oseen flow in external domains

Abstract

This work serves as an introductory exploration of Oseen flow, a mathematical and physical framework for modeling fluid dynamics, with a specific focus on viscous substances like liquids or gases. The presented theorem and its associated lemmas are an extension of the foundational theory of potential flow, which is conventionally applied to inviscid fluids. The primary goal in investigating Oseen flow within external domains is to elucidate the influence of viscous effects on flow patterns beyond solid structures. As a result, we prove the existence of generalized solutions when  is a three-dimensional (3D) domain in Stokes problem.