Asymptotic Properties of Linearized Equations of Low Compressible Fluid Motion

TL;DR

This paper investigates the behavior of solutions to linearized equations of low compressible fluid motion, establishing existence, uniqueness, and convergence to incompressible flow as compressibility diminishes.

Contribution

It provides rigorous analysis of weak solutions for the linearized viscous fluid equations and demonstrates their convergence to incompressible flow in the zero compressibility limit.

Findings

Existence and uniqueness of weak solutions are proven.

Solutions converge to incompressible flow as compressibility approaches zero.

Estimates for solutions are derived.

Abstract

Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions towards the incompressible limit when compressibility tends to zero is studied.