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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).
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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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