On the global existence and stability of 3-D viscous cylindrical circulatory flows. (English) Zbl 1449.35342

The main result in this paper is a global existence and uniqueness theorem of cylindrical symmetric circulatory flows for the three-dimensional compressible Navier-Stokes equations. It is also shown that the flow is globally stable in time when the corresponding initial states are perturbed suitably small. The proof follows from the local existence result of classical solutions, continuity arguments, and is essentially based on uniform weighted energy estimates.


35Q30 Navier-Stokes equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35L70 Second-order nonlinear hyperbolic equations