Differential and Integral Equations

On the global well-posedness of 3-d Navier-Stokes equations with vanishing horizontal viscosity

Hammadi Abidi and Marius Paicu

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Abstract

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.

Article information

Source
Differential Integral Equations Volume 31, Number 5/6 (2018), 329-352.

Dates
First available in Project Euclid: 23 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1516676426

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30] 76D09: Viscous-inviscid interaction

Citation

Abidi, Hammadi; Paicu, Marius. On the global well-posedness of 3-d Navier-Stokes equations with vanishing horizontal viscosity. Differential Integral Equations 31 (2018), no. 5/6, 329--352. https://projecteuclid.org/euclid.die/1516676426


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