# Artificial boundary conditions for linearized stationary incompressible viscous flow around rotating and translating body

## TL;DR

This paper develops and analyzes artificial boundary conditions for linearized and nonlinear stationary incompressible viscous flow around rotating and translating bodies, providing pressure estimates and error bounds for truncated computational domains.

## Contribution

It introduces artificial boundary conditions for exterior flow problems and derives error estimates comparing truncated and full domain solutions.

## Key findings

- Pressure pointwise estimates for both linearized and nonlinear flows.
- Error bounds for solutions in truncated domains with artificial boundary conditions.
- Comparison results between truncated and full domain solutions.

## Abstract

We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain B with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain B_R of the exterior domain B under certain artificial boundary conditions on the truncating boundary and then compare this solution with the solution in the exterior domain B to get the truncation error estimate.