On the global well-posedness of 3-D Navier-Stokes equations with vanishing horizontal viscosity. (English) Zbl 1449.35347

Abidi, Hammadi; Paicu, Marius

Differ. Integral Equ. 31, No. 5-6, 329-352 (2018).

Summary: We study, in this paper, the axisymmetric 3-D Navier-Stokes system where the horizontal viscosity is zero. We prove the existence of a unique global solution to the system with initial data in Lebesgue spaces.

MSC:

35Q35	PDEs in connection with fluid mechanics
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
76D09	Viscous-inviscid interaction

Keywords:

axisymmetric Navier-Stokes system; axisymmetric solenoidal vector-field; Biot-Savart law