# A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers

### Reinhard Farwig

Technische Hochschule Darmstadt, Germany### Milan Pokorný

Charles University, Praha, Czech Republic

## Abstract

Consider the flow of a compressible Newtonian fluid around or past a rotating rigid obstacle in ${\mathbb R}^3.$ After a coordinate transform to get a problem in a time-independent domain we assume the new system to be stationary, then linearize and - in this paper dealing with the whole space case only - use Fourier transform to prove the existence of solutions $u$ in $L^q$-spaces. However, the solution is constructed first of all in terms of $g=\mathrm {div}\, u$, explicit in Fourier space, and is in contrast to the incompressible case not based on the heat kernel, but requires the analysis of new multiplier functions related to Bochner-Riesz multipliers and leading to the restriction $\frac{6}{5}<q<6$.

## Cite this article

Reinhard Farwig, Milan Pokorný, A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers. Z. Anal. Anwend. 34 (2015), no. 3, pp. 285–308

DOI 10.4171/ZAA/1540