Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equa\-tions
From MaRDI portal
Publication:2573497
DOI10.1016/j.jfa.2005.06.009zbMath1083.35110OpenAlexW2043123366MaRDI QIDQ2573497
Publication date: 22 November 2005
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2005.06.009
PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05)
Related Items
Regularity criteria for the 3D MHD equations in term of velocity ⋮ On the energy equality for very weak solutions to 3D MHD equations ⋮ The 2D magnetohydrodynamic equations with magnetic diffusion ⋮ Partial regularity of suitable weak solutions to the four-dimensional incompressible magneto-hydrodynamic equations ⋮ Decay properties of solutions to the incompressible magnetohydrodynamics equations in a half space ⋮ Partial regularity criteria for suitable weak solutions of the three-dimensional liquid crystals flow ⋮ Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion ⋮ Improved regularity criteria for the MHD equations in terms of pressure using an Orlicz norm ⋮ A LOGARITHMALLY IMPROVED BLOW-UP CRITERION OF SMOOTH SOLUTIONS FOR THE THREE-DIMENSIONAL MHD EQUATIONS ⋮ Energy conservation and regularity for the 3D magneto-hydrodynamics equations ⋮ Well-posedness and attractors of the multi-dimensional hyperviscous magnetohydrodynamic equations ⋮ On the large data global well-posedness of inviscid axially symmetric MHD-Boussinesq system ⋮ Global solutions to the damped MHD system ⋮ On the blow-up criterion for the Hall-MHD problem with partial dissipation in \(\mathbb{R}^3\) ⋮ Asymptotic regularity for the generalized MHD‐Boussinesq equations ⋮ On the interior regularity criterion for suitable weak solutions to the 3d magneto-hydrodynamics equations in terms of the velocity gradient ⋮ The regularity of very weak solutions to magneto-hydrodynamics equations ⋮ Optimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equations ⋮ The local characterizations of the singularity formation for the MHD equations ⋮ Hall effect on the asymptotic stability of the planar compressible MHD flows ⋮ Unnamed Item ⋮ Remark on the regularity for weak solutions to the magnetohydrodynamic equations ⋮ A regularity criterion for two-and-half-dimensional magnetohydrodynamic equations with horizontal dissipation and horizontal magnetic diffusion ⋮ Sharp time decay rates of H 1 weak solutions for the 2D MHD equations with linear damping velocity ⋮ Boundary layer problem of MHD system with non-characteristic perfect conducting wall ⋮ Viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow with diffusion ⋮ On the regularity of weak solutions of the MHD equations in BMO −1 and Ḃ∞,∞−1 ⋮ Energy cascades in physical scales of 3D incompressible magnetohydrodynamic turbulence ⋮ Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion ⋮ An energy-preserving MAC-Yee scheme for the incompressible MHD equation ⋮ Space-time decay estimates for the incompressible viscous resistive MHD and Hall-MHD equations ⋮ On the regularity of the axially symmetric solutions to the three-dimensional MHD equations ⋮ Regularity Theory for the Dissipative Solutions of the MagnetoHydroDynamic Equations ⋮ Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations ⋮ Vanishing viscosity limit for the 3D magnetohydrodynamic system with generalized Navier slip boundary conditions ⋮ On regularity criterion to the 3D axisymmetric incompressible MHD equations ⋮ Remarks on the blow-up criteria for three-dimensional ideal magnetohydrodynamics equations ⋮ Blow-up criterion for two-dimensional magneto-micropolar fluid equations with partial viscosity ⋮ THE ARTIFICIAL COMPRESSIBILITY APPROXIMATION FOR MHD EQUATIONS IN UNBOUNDED DOMAIN ⋮ On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipation ⋮ Global Well-posedness of two-dimensional Magnetohydrodynamic Flows with Partial Dissipation and Magnetic Diffusion ⋮ Global Small Solution to the 2D MHD System with a Velocity Damping Term ⋮ Regularity criteria of axisymmetric weak solutions to the 3D MHD equations ⋮ Decoupled schemes for unsteady MHD equations. I. time discretization ⋮ Blow-up Criteria for the 2D Full Compressible MHD system ⋮ Serrin-type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component ⋮ Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov-Sobolev-type spaces ⋮ On partial regularity criterion for the co-rotational Beris-Edwards system modeling nematic liquid crystal flow ⋮ Suitable weak solutions of the incompressible magnetohydrodynamic equations in time varying domains ⋮ On 2-D Boussinesq equations for MHD convection with stratification effects ⋮ A regularity criterion for the 3D MHD equations in a local BMO space ⋮ On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces ⋮ Well posedness of magnetohydrodynamic equations in 3D mixed-norm Lebesgue space ⋮ Global well-posedness for MHD system with mixed partial dissipation and magnetic diffusion in \(2 \frac{1}{2}\) dimensions ⋮ On the regularity criteria for weak solutions to the magnetohydrodynamic equations ⋮ Singularity formation for the incompressible Hall-MHD equations without resistivity ⋮ The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations ⋮ Blow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosity ⋮ Diffusion vanishing limit of the nonlinear pipe magnetohydrodynamic flow with fixed viscosity ⋮ The MHD equations in the Lorentz space with time dependent external forces ⋮ Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space ⋮ The energy conservations and lower bounds for possible singular solutions to the 3D incompressible MHD equations ⋮ On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation ⋮ Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data ⋮ Global weighted regularity for the 3D axisymmetric MHD equations ⋮ Global well-posedness for the incompressible MHD equations with variable viscosity and conductivity ⋮ Global axisymmetric solutions to the 3D MHD equations with nonzero swirl ⋮ Regularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equations ⋮ Analysis of coupling iterations based on the finite element method for stationary magnetohydrodynamics on a general domain ⋮ Liouville theorem for MHD system and its applications ⋮ Global regularity for a class of generalized magnetohydrodynamic equations ⋮ Non blow-up criterion for the 3-D magneto-hydrodynamics equations in the limiting case ⋮ Lie group solutions of magnetohydrodynamics equations and their well-posedness ⋮ On regularity for the 3D MHD equations via one directional derivative of the pressure ⋮ A note on blow-up criterion of the 3d magnetic Bénard equations ⋮ Global solution of 3D axially symmetric nonhomogeneous incompressible MHD equations ⋮ Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects ⋮ On the regularity criteria for the 3D magneto-micropolar fluids in terms of one directional derivative ⋮ Optimal \(L^2\) decay of the magneto-micropolar system in \(\mathbb{R}^3\) ⋮ Zero viscosity and diffusion vanishing limit of the incompressible magnetohydrodynamic system with perfectly conducting wall ⋮ Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion ⋮ Magneto-hydrodynamical model for plasma ⋮ Hausdorff measure of boundary singular points in the magnetohydrodynamic equations ⋮ On the existence, uniqueness and regularity of solutions for a class of MHD equations of non-Newtonian type ⋮ Regularity criteria in terms of the pressure for the three-dimensional MHD equations ⋮ Blow-up criterion for compressible MHD equations ⋮ Local regularity of the magnetohydrodynamics equations near the curved boundary ⋮ On 3D MHD equations with regularity in one directional derivative of the velocity ⋮ Global strong solution to the three-dimensional density-dependent incompressible magnetohydrodynamic flows ⋮ Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space ⋮ On the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosity ⋮ Global existence of solutions for the thermoelastic Bresse System ⋮ A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion ⋮ On the local smoothness of weak solutions to the MHD system ⋮ Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density ⋮ A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows ⋮ Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations ⋮ Global well-posedness of the 3D incompressible MHD equations with variable density ⋮ On the partial regularity theory for the MHD equations ⋮ Stability of axially-symmetric solutions to incompressible magnetohydrodynamics with no azimuthal velocity and with only azimuthal magnetic field ⋮ Global well-posedness for magneto-micropolar system in \(2 \frac{1}{2}\) dimensions ⋮ Blowup mechanism for viscous compressible heat-conductive magnetohydrodynamic flows in three dimensions ⋮ On the global regularity for the 3D magnetohydrodynamics equations involving partial components ⋮ Property of solution to axially symmetric incompressible MHD equations in three dimensions ⋮ Refined regularity class of suitable weak solutions to the 3D magnetohydrodynamics equations with an application ⋮ Interior condition on suitable weak solutions to the 3D MHD equations via pressure ⋮ Blow-up criteria and regularity criterion for the three-dimensional magnetic Bénard system in the multiplier space ⋮ The 3D incompressible magnetohydrodynamic equations with fractional partial dissipation ⋮ A remark on the existence of a class of stretched \(2 \frac{1}{2} D\) magnetohydrodynamics flow ⋮ Large time decay of solutions for the 3D magneto-micropolar equations ⋮ Weighted regularity criteria of weak solutions to the incompressible 3D MHD equations ⋮ Global well-posedness of the two-dimensional incompressible magnetohydrodynamics system with variable density and electrical conductivity ⋮ Two regularity criteria for the 3D MHD equations ⋮ A Beale-Kato-Madja criterion for magneto-micropolar fluid equations with partial viscosity ⋮ Remarks on partial regularity for suitable weak solutions of the incompressible magnetohydrodynamic equations ⋮ Decoupled schemes for unsteady MHD equations. II: Finite element spatial discretization and numerical implementation ⋮ On partial regularity problem for 3D Boussinesq equations ⋮ Boundary layer problem and zero viscosity-diffusion limit of the incompressible magnetohydrodynamic system with no-slip boundary conditions ⋮ Hausdorff measure of the singular set in the incompressible magnetohydrodynamic equations ⋮ Some regularity criteria for the 3D incompressible magnetohydrodynamics ⋮ The tamed MHD equations ⋮ On the role of pressure in the theory of MHD equations ⋮ Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity ⋮ New \(\varepsilon \)-regularity criteria of suitable weak solutions of the 3D Navier-Stokes equations at one scale ⋮ Initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection ⋮ A new sufficient condition for local regularity of a suitable weak solution to the MHD equations ⋮ Global well-posedness for the 3D incompressible inhomogeneous Navier-Stokes equations and MHD equations ⋮ Global regularity for the \(2\frac{1}{2}\)D incompressible Hall-MHD system with partial dissipation ⋮ Global existence and asymptotic stability of 3D generalized magnetohydrodynamic equations ⋮ Global smooth axisymmetic solutions of the Boussinesq equations for magnetohydrodynamics convection ⋮ Axially symmetric incompressible MHD in three dimensions ⋮ Global weak solutions for the two-dimensional magnetohydrodynamic equations with partial dissipation and diffusion ⋮ New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure ⋮ Global well-posedness of a 3D MHD model in porous media ⋮ The combined inviscid and non-resistive limit for the nonhomogeneous incompressible magnetohydrodynamic equations with Navier boundary conditions ⋮ Interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations ⋮ Vanishing viscosity limit for the 3D magnetohydrodynamic system with a slip boundary condition ⋮ Convergence analysis of a conservative finite element scheme for the thermally coupled incompressible inductionless MHD problem ⋮ Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem ⋮ Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the \(L^p\) framework ⋮ Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary ⋮ Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces ⋮ On axially symmetric incompressible magnetohydrodynamics in three dimensions ⋮ Partial regularity for the 3D magneto-hydrodynamics system with hyper-dissipation ⋮ Global solution to the 3D nonhomogeneous incompressible MHD equations with some large initial data
Cites Work
- Unnamed Item
- Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
- Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
- Partial regularity of solutions to the Navier-Stokes equations
- Gradient estimation on Navier-Stokes equations
- Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain
- On the regularity of weak solutions to the magnetohydrodynamic equations
- Inéquations en thermoélasticité et magnétohydrodynamique
- Some mathematical questions related to the mhd equations
- On partial regularity results for the navier-stokes equations
- A new proof of the Caffarelli-Kohn-Nirenberg theorem
- Partial regularity of suitable weak solutions of the navier-stokes equations
