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

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 $\frac{6}{5}<q<6$.