Vertex circulation and regularity of compressible Stokes flows: Numerical simulations

The vertex can be a junction point that inflow and outflow meet and may result in a vertex circulation that means a cone-like rotation at vertex. The vertex circulation by compressible Stokes flows may blow up due to the singular behavior of suddenly change at corner. The angular velocity component is found to be positive while for λ ∈ (0, 1) the velocity vector itself vanishes at the vertex and the pressure blows up there. We also demonstrate this phenomena by numerical simulations.