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

Yin, Huicheng; Lin, Zhang

Differ. Integral Equ. 32, No. 5-6, 337-358 (2019).

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.

Reviewer: Radu Precup (Cluj-Napoca)

MSC:

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

Keywords:

Navier-Stokes equations; compressible fluid; global existence; weighted energy estimate; stability