A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner-Riesz Multipliers
2015
Abstract
Consider the flow of a compressible Newtonian fluid around or past a rotating rigid obstacle in 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 = 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 6/5 < q < 6.