Some regularity criteria for the 3D generalized Navier-Stokes equations
type: Item
instance of: scholarly article
title: Some regularity criteria for the 3D generalized Navier-Stokes equations
zbMATH Open document ID: 1472.35301
author: Jae-Myoung Kim
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-05-19T00:00:00Z
review text: Generalizations and improvements of Serrin's type regularity criterion for weak solutions of the three-dimensional Navier-Stokes system with the dissipation defined by fractional Laplacians are shown. These are conditions expressed in terms of the vorticity of solutions using Lorentz spaces.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 7349847
zbMATH Keywords: Navier-Stokes system
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: regularity of solutions
zbMATH Keywords: Serrin's criterion
MaRDI profile type: Publication
full work available at URL: s00033-021-01549-z
OpenAlex ID: W3160270982
cites work: A weak-\(L^p\) Prodi-Serrin type regularity criterion for the Navier-Stokes equations
cites work: On the regularity conditions for the Navier-Stokes and related equations
cites work: On the geometric regularity conditions for the 3D Navier-Stokes equations
cites work: A maximum principle applied to quasi-geostrophic equations
cites work: Ill-posedness of Leray solutions for the hypodissipative Navier-Stokes equations
cites work: Global regularity for the hyperdissipative Navier-Stokes equation below the critical order
cites work: Geometric Statistics in Turbulence
cites work: Effect of vorticity coherence on energy-enstrophy bounds for the 3D Navier-Stokes equations
cites work: Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations
cites work: On the regularity criteria for the generalized Navier-Stokes equations and Lagrangian averaged Euler equations.
cites work: Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations
cites work: Uniform local well-posedness for the density-dependent magnetohydrodynamic equations
cites work: Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations
cites work: A regularity criterion for the 3D generalized MHD equations
cites work: On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects
cites work: RETRACTED ARTICLE: ``Local well-posedness for the incompressible full magneto-micropolar system with vacuum''
cites work: On regularity criteria for the 2D generalized MHD system
cites work: Commutator estimates with fractional derivatives and local existence for the generalized MHD equations
cites work: Notes on the geometric regularity criterion of 3D Navier-Stokes system
cites work: A weak-\(L^{p}\) Prodi-Serrin type regularity criterion for the micropolar fluid equations
cites work: On the regularity of generalized MHD equations
cites work: Convolution operators and L(p, q) spaces
cites work: Direction of vorticity and a refined regularity criterion for the Navier-Stokes equations with fractional Laplacian
cites work: Some new regularity criteria for the 3D MHD equations
cites work: A new regularity criterion for the 3D generalized Hall-MHD system with \(\beta \in (\frac{1}{2}, 1]\)
cites work: On Prodi-Serrin type conditions for the 3D Navier-Stokes equations
cites work: A geometric interpretation of coherent structures in Navier–Stokes flows
cites work: Q5607484
cites work: Q3336200
cites work: Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems
cites work: Global well-posedness for the 3D incompressible Hall-magnetohydrodynamic equations with Fujita-Kato type initial data
cites work: Global well-posedness, BKM blow-up criteria and zero \(h\) limit for the 3D incompressible Hall-MHD equations
cites work: Balance of the vorticity direction and the vorticity magnitude in 3D fractional Navier-Stokes equations
cites work: Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
cites work: Generalized MHD equations.
cites work: Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity
cites work: Regularity criteria for the generalized viscous MHD equations
cites work: Logarithmically improved regularity criteria for the 3D viscous MHD equations
DOI: 10.1007/S00033-021-01549-Z
description: scientific article; zbMATH DE number 7349847