The linearized 3D Euler equations with inflow, outflow

TL;DR

This paper extends the analysis of linearized 3D Euler equations with inflow and outflow boundary conditions to multiply connected domains, establishing conditions for higher regularity solutions.

Contribution

It generalizes previous results to more complex domains and defines compatibility conditions for initial data to achieve higher regularity.

Findings

Extended linearized Euler equations to multiply connected domains

Established compatibility conditions for initial data

Achieved higher regularity solutions under new conditions

Abstract

In 1983, Antontsev, Kazhikhov, and Monakhov published a proof of the existence and uniqueness of solutions to the 3D Euler equations in which on certain inflow boundary components fluid is forced into the domain while on other outflow components fluid is drawn out of the domain. A key tool they used was the linearized Euler equations in vorticity form. We extend their result on the linearized problem to multiply connected domains and establish compatibility conditions on the initial data that allow higher regularity solutions.