Invariance of stochastic control systems with deterministic arguments

An evolution compressible Stokes system is studied in polygon. A lowest order corner singularity by the Laplacian operator is sorted out and an increased regularity is established in a suitable Banach space. In the lowest level, for each time the order of the corner singularity of the system is the same as that of the Laplacian. In addition, a singular function for pressure is defined and shows that the corner singularities originated from the corners of polygon may propagate along the directed streamlines.