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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 3, 2015, pp. 285–308
DOI: 10.4171/ZAA/1540

Published online: 2015-07-08

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

Reinhard Farwig[1] and Milan Pokorný[2]

(1) Technische Hochschule Darmstadt, Germany
(2) Charles University, Praha, Czech Republic

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}

Keywords: Compressible Navier-Stokes equations, linearization, modified Bochner–Riesz multipliers, rotating body

Farwig Reinhard, Pokorný Milan: A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers. Z. Anal. Anwend. 34 (2015), 285-308. doi: 10.4171/ZAA/1540