Decomposition of vector-valued divergence free Sobolev functions and shape optimization for stationary Navier-Stokes equations

Gengsheng Wang, Donghui Yang

We establish a divergence free partition for vector-valued Sobolev functions with free divergence in ${\mathbf{R}}^n,n\ge 1$. We prove that for any domain $\om$ of class $\mathcal{C}$ in $…