Compressible Navier--Stokes System with Transport Noise

We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both continuity as well momentum equation. focus on three different situations: (i) is smooth time and equations are understood sense of classical weak deterministic theory, (ii) rough we interpret framework paths with unbounded drivers, (iii) have Brownian Stratonovich type study existence martingale solutions. The first situation serves an approximation for (iii), while motivated recent results incompressible concerning physical modeling regularization noise.