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Author:

Liu, Jitao (Liu, Jitao.) (Scholars:刘继涛) | Niu, Dongjuan (Niu, Dongjuan.)

Indexed by:

Scopus SCIE

Abstract:

In this paper, we investigate the global well-posedness of three-dimensional Navier-Stokes equations with horizontal viscosity under a special symmetric structure: helical symmetry. More precisely, by a revised Ladyzhenskaya-type inequality and utilizing the behavior of helical flows, we prove the global existence and uniqueness of weak and strong solutions to the three-dimensional helical flows. Our result reveals that for the issue of global well-posedness of the viscous helical flows, the horizontal viscosity plays the important role. To some extent, our work can be seen as a generalization of the result by Mahalov et al. (Arch Ration Mech Anal 112(3): 193-222, 1990).

Keyword:

Helical symmetry Global well-posedness Navier-Stokes equations Horizontal viscosity

Author Community:

  • [ 1 ] [Liu, Jitao]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 2 ] [Niu, Dongjuan]Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

Reprint Author's Address:

  • 刘继涛

    [Liu, Jitao]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

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Source :

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

ISSN: 0044-2275

Year: 2017

Issue: 3

Volume: 68

2 . 0 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:66

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 3

SCOPUS Cited Count: 3

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 8

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