On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is mixed elliptic–hyperbolic changes type suitable formulation boundary conditions at boundaries great importance. First, we establish existence uniqueness spiral solutions with nonzero angular velocity vorticity which close to background flow small Bernoulli’s function entropy outer cylinder angles both inner cylinders independent axis, it shown that this case, sonic points nonexceptional noncharacteristically degenerate, form surface. Second, also prove rotational adjacent flow, whose an key elements our analysis utilize deformation-curl decomposition for steady Euler deal hyperbolicity subsonic regions find appropriate multiplier linearized second-order equations crucial identify yield important basic energy estimates.