JournalszaaVol. 34, No. 3pp. 285–308

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

Consider the flow of a compressible Newtonian fluid around or past a rotating rigid obstacle in R3.{\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 uu in LqL^q-spaces. However, the solution is constructed first of all in terms of g=divug=\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 65<q<6\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