Shape Optimization in Two-Dimensional Viscous Compressible Fluids

We present a method for solving the optimal shape problems for profiles surrounded byviscous compressible fluids in two space dimensions. The class of admissible profiles is quite generalincluding the minimal volume condition and a constraint on the thickness of the boundary. The fluidflow is modelled by the Navier-Stokes system for a general viscous barotropic fluid with the pressuresatisfying p(ρ) = aρlog~d(ρ) for large ρ. Here d > 1 and a > 0.