Numerical method for drag minimization in compressible flows

In the series of papers the mathematical theory of shape optimization for compressible Navier-Stokes inhomo-geneous boundary value problems is developed. The key part of the theory include the new results on the existence and shape differentiability of the weak solutions to compressible Navier-Stokes equations. In particular, our results lead to the rigorous mathematical framework for the drag minimization of an obstacle in the flow of gas with small adiabatic constant.