Regularity criteria for the generalized viscous MHD equations

From MaRDI portal
Publication:2466260

DOI10.1016/j.anihpc.2006.03.014zbMath1130.35110OpenAlexW2067166379MaRDI QIDQ2466260

Yong Zhou

Publication date: 14 January 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2007__24_3_491_0




Related Items

Note on energy equality of MHD systemGlobal well-posedness and analyticity results to 3-D generalized magnetohydrodynamic equationsGlobal well-posedness for MHD system with mixed partial dissipation and magnetic diffusion in \(2 \frac{1}{2}\) dimensionsErgodicity of stochastic magneto-hydrodynamic equations driven by \(\alpha\)-stable noiseA new regularity criterion for the 3D generalized Hall-MHD system with \(\beta \in (\frac{1}{2}, 1\)] ⋮ On well-posedness of generalized Hall-magneto-hydrodynamicsWell-posedness and stability for the generalized incompressible magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spacesGlobal existence of strong solutions for the generalized Navier-Stokes equations with dampingA regularity criterion for the generalized Hall-MHD systemOn smoothness of 3D generalized MHD equationsGlobal axisymmetric solutions to the 3D MHD equations with nonzero swirlRegularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equationsCoriolis effect on temporal decay rates of global solutions to the fractional Navier-Stokes equationsPullback attractor and invariant measures for the three-dimensional regularized MHD equationsNon-uniqueness of weak solutions to 3D magnetohydrodynamic equationsLogarithmically improved regularity criteria for the Navier-Stokes and MHD equationsA regularity criterion for a generalized Hall-MHD systemOn regularity for the 3D MHD equations via one directional derivative of the pressureA note on blow-up criterion of the 3d magnetic Bénard equationsGeneralized MHD system with velocity gradient in Besov spaces of negative orderNumerical simulation of multidimensional nonlinear fractional Ginzburg-Landau equationsNote on solution regularity of the generalized magnetohydrodynamic equations with partial dissipationOn the Cauchy problem for a Leray-\(\alpha \)-MHD modelOn global regularity of 2D generalized magnetohydrodynamic equationsGlobal regularity for MHD Sisko fluid in annular pipeRemarks on the regularity criteria for generalized MHD equationsA regularity criterion for the 3D MHD equations in terms of the gradient of the pressure in the multiplier spacesConditional regularity for the 3D MHD equations in the critical Besov spaceTwo regularity criteria to the 2D generalized MHD equations with zero magnetic diffusivityGlobal well-posedness for the generalized magneto-hydrodynamic equations in the critical Fourier-Herz spacesDispersive effect of the Coriolis force and the local well-posedness for the fractional Navier-Stokes-Coriolis systemOn the global regularity of two-dimensional generalized magnetohydrodynamics systemRegularity criteria for a Lagrangian-averaged magnetohydrodynamic-\(\alpha \) modelA new regularity criterion in terms of the direction of the velocity for the MHD equationsGlobal smooth solutions of the 2D MHD equations for a class of large data without magnetic diffusionLimiting case for the regularity criterion to the 3-D magneto-hydrodynamics equationsRegularity criteria for the 3D generalized MHD and Hall-MHD systemsRegularity criteria for the three-dimensional MHD equationsWell-posedness for the fractional Landau-Lifshitz equation without Gilbert dampingRegularity criteria in terms of the pressure for the Navier-Stokes equations in the critical Morrey-Campanato spaceA regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spacesWeak-strong uniqueness for the generalized Navier-Stokes equationsWeak attractors for the dissipative fractional Heisenberg equationSome new regularity criteria for the 3D MHD equationsOn the Navier-Stokes equations in scaling-invariant spaces in any dimensionSpace-time regularity of the \textit{mild} solutions to the incompressible generalized Navier-Stokes equations with small rough initial dataOn the regularity criterion for the 3D generalized MHD equations in Besov spacesAn improved regularity criterion for the 3D Hall-MHD equations via the vorticityTime decay rate of weak solutions to the generalized MHD equations in \(\mathbb{R}^2\)A new regularity criterion for the three-dimensional incompressible magnetohydrodynamic equations in the Besov spacesA remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosityInterior condition on suitable weak solutions to the 3D MHD equations via pressureGlobal well-posedness of the generalized magnetohydrodynamic equationsGlobal regularity to the 3D generalized MHD equations with large initial dataUniqueness of weak solution to the generalized magneto-hydrodynamic systemGlobal well-posedness of 2D generalized MHD equations with fractional diffusionBlow-up criteria for smooth solutions to the generalized 3D MHD equationsA new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity fieldA note on the blow-up criterion of smooth solutions to the 3D incompressible MHD equationsTwo regularity criteria for the 3D MHD equationsA regularity criterion for the 3D generalized MHD equationsA Beale-Kato-Madja criterion for magneto-micropolar fluid equations with partial viscosityRegularity criteria of MHD system involving one velocity and one current density componentUniqueness of weak solutions for fractional Navier-Stokes equationsRegularity criteria and small data global existence to the generalized viscous Hall-magnetohydrodynamicsRegularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato spaceOn regularity criteria for the three-dimensional micropolar fluid equations in the critical Morrey-Campanato spaceExistence theorem and regularity criteria for the generalized MHD equationsFractional Navier-Stokes equations and a Hölder-type inequality in a sum of singular spacesOn the regularity of generalized MHD equationsNotes on the global well-posedness for the Maxwell-Navier-Stokes systemA regularity criterion for the nematic liquid crystal flowsRegularity criteria for the solutions to the 3D MHD equations in the multiplier spaceGlobal well posedness for the Maxwell-Navier-Stokes system in 2DGlobal smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datumMHD equations with regularity in one directionRemarks on global regularity of 2D generalized MHD equationsThe 3D Boussinesq equations with regularity in one directional derivative of the pressureOn the 3D ideal MHD equations with partial dampingGeneralized Navier-Stokes equations with initial data in local \(Q\)-type spacesWell-posedness for the generalized Navier-Stokes-Landau-Lifshitz equationsCommutator estimates with fractional derivatives and local existence for the generalized MHD equationsA double-logarithmically improved regularity criterion of weak solutions for the 3D MHD equationsSome regularity criteria for the 3D generalized Navier-Stokes equationsWell-posedness and decay of solutions to 3D generalized Navier-Stokes equationsGlobal regularity of 2D generalized MHD equations with magnetic dampingRemarks on pressure regularity criterion for the 3D Boussinesq equationsA logarithmic regularity criterion for the two-dimensional MHD equationsGlobal well-posedness and decay results to 3D generalized viscous magnetohydrodynamic equationsRefined blow-up criteria for the full compressible Navier-Stokes equations involving temperatureDecay rate of global solutions to three dimensional generalized MHD systemRegularity criteria for the 3D generalized MHD equations in terms of vorticityLong time behavior of solutions to 3D generalized MHD equationsRegularity criteria for 3D generalized incompressible magneto-micropolar fluid equationsA new regularity criterion for the 3D incompressible MHD equations via partial derivativesGlobal regularity of \(n\) dimensional generalized MHD equations without magnetic diffusionWell-posedness and decay of solutions for three-dimensional generalized Navier-Stokes equationsGlobal regularity of the logarithmically supercritical MHD system with zero diffusivity\((N-1)\) velocity components condition for the generalized MHD system in \(N\)-dimensionGlobal regularity of \(N\)-dimensional generalized MHD system with anisotropic dissipation and diffusionWell-posedness for fractional Navier-Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn)ON THE REGULARITY CRITERIA FOR THE GENERALIZED VISCOUS MHD EQUATIONSOn regularity criteria for the 2D generalized MHD systemOn regularity criteria for the 3D Hall-MHD equations in terms of the velocityBlow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosityOn regularity criteria in terms of pressure for the 3D viscous MHD equationsLogarithmically improved regularity criteria for the 3D viscous MHD equationsDirection of vorticity and a refined regularity criterion for the Navier-Stokes equations with fractional LaplacianWell-posedness and dynamics of the stochastic fractional magneto-hydrodynamic equationsA new Beale-Kato-Majda criteria for the 3D magneto-micropolar fluid equations in the Orlicz-Morrey spaceRemarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipationAsymptotic behavior, regularity criterion and global existence for the generalized Navier-Stokes equationsGlobal solutions to three-dimensional generalized MHD equations with large initial dataA regularity criterion for the 3D generalized MHD system involving partial componentsA new blowup criterion for a generalized Hall-MHD system concerning the deformation tensorOn 3D generalized MHD equations with different dissipation exponentsUnnamed ItemOn vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall‐MHD systemOn regularity criteria for MHD system in anisotropic Lebesgue spacesOptimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equationsBlow-up criterion for compressible MHD equationsDetermining modes and determining nodes for the 3D non-autonomous regularized magnetohydrodynamics equationsOn the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosityGlobal existence of strong solutions to incompressible MHDGlobal existence of solutions for the thermoelastic Bresse SystemGlobal regularity of the two-dimensional incompressible generalized magnetohydrodynamics systemRemarks on the regularity criteria of generalized MHD and Navier-Stokes systemsRefined blow-up criterion for the 3D magnetohydrodynamics equationsFractional Navier–Stokes regularity criterion involving the positive part of the intermediate eigenvalue of the strain matrixBlow-up of smooth solutions to the isentropic compressible MHD equationsOn the uniqueness of weak solutions of the 3D MHD equations in the Orlicz–Morrey spaceRemarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field componentsA regularity criterion for the density-dependent magnetohydrodynamic equationsA logarithmic regularity criterion for the 3D generalized MHD systemUnnamed ItemGlobal existence of solutions to the 2D incompressible liquid crystal flow with fractional diffusionLogarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equationsGlobal existence of discretely self-similar solutions to the generalized MHD system in Besov spaceOn the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipationGlobal regularity of 3D generalized incompressible magnetohydrodynamic-\(\alpha\) modelSpace-time regularity of the solutions to MHD equations with small rough dataGlobal existence of strong solutions to incompressible MHDBlow-up Criteria for the 2D Full Compressible MHD systemRegularity criteria for unsteady MHD third grade fluid due to rotating porous disk



Cites Work