On steady solutions to the MHD equations with inhomogeneous generalized impermeability boundary conditions for the magnetic field
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DOI: 10.1002/mma.10252
Abstract: The paper deals with the steady MHD equations for a viscous incompressible fluid in a bounded and generally multiply connected domain Ω⊂ℝ3$$ \Omega \subset {\mathrm{\mathbb{R}}}^3 $$ with the no‐slip boundary condition for the velocity u$$… read more here.
Keywords: inhomogeneous generalized; mhd equations; generalized impermeability; impermeability boundary ... See more keywords
Analysis on the Regularity of Solutions of Energy Conservation to the Compressible MHD Equations
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DOI: 10.1002/mma.70163
Abstract: In our article, we give some sufficient conditions on the regularity of solutions to the compressible magnetohydrodynamics (MHD) equations on 𝕋d (d ≥$$ \ge $$ 2) for the point‐wise energy conservation, which is different from… read more here.
Keywords: energy; mhd equations; regularity solutions; analysis regularity ... See more keywords
Well-posedness for the Incompressible Hall-MHD Equations in Low Regularity Spaces
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DOI: 10.1007/s00009-018-1096-x
Abstract: In this paper, we first establish the local well-posedness of strong solutions to the Cauchy problem of the incompressible viscous resistive Hall-MHD equations in $$H^s(\mathbb {R}^3)$$Hs(R3)$$(\frac{3}{2}< s\le \frac{5}{2})$$(32 read more here.
Keywords: well posedness; mhd equations; posedness incompressible; hall mhd ... See more keywords
On the Blow-Up Criterion for Incompressible Stokes–MHD Equations
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DOI: 10.1007/s00025-018-0874-x
Abstract: Our aim is to establish a blow-up criterion for the local strong solutions in terms of the gradient of the magnetic field only in $$\textit{BMO}$$BMO spaces. read more here.
Keywords: stokes mhd; criterion; blow criterion; mhd equations ... See more keywords
Liouville-type theorems for the 3D stationary Navier-Stokes, MHD and Hall-MHD equations
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DOI: 10.1016/j.jmaa.2020.124343
Abstract: Abstract In this paper, we consider the Liouville-type problem of the three dimensional stationary incompressible Navier-Stokes equations, and establish an improved Liouville-type result only under the condition that the L p norm of a velocity… read more here.
Keywords: mhd equations; mhd hall; liouville type; navier stokes ... See more keywords
Decay-in-time of the Highest-order Derivatives of Solutions for the Compressible Isentropic MHD Equations
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DOI: 10.1016/j.jmaa.2021.125273
Abstract: Abstract In this paper, we consider the large time behavior of the Cauchy problem for the three-dimensional isentropic compressible magnetohydrodynamic (MHD) equations. The global existence of smooth solutions for the 3D compressible MHD equations has… read more here.
Keywords: time; mhd; mhd equations; compressible mhd ... See more keywords
Improved regularity criteria for the MHD equations
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DOI: 10.1063/5.0179393
Abstract: In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32 read more here.
Keywords: improved regularity; regularity criteria; mhd equations; criteria mhd ... See more keywords
Uniform attractors for 3D MHD equations with nonlinear damping
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DOI: 10.1080/00036811.2024.2305837
Abstract: ABSTRACT The aim of this paper is to investigate the uniform attractors for 3D MHD equations with nonlinear damping. Some uniform estimates for strong solutions are established. Furthermore, we prove that 3D damped equations have… read more here.
Keywords: nonlinear damping; mhd equations; uniform attractors; attractors mhd ... See more keywords
On Liouville-type theorems for the 2D stationary MHD equations
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DOI: 10.1088/1361-6544/ac3f8b
Abstract: We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function… read more here.
Keywords: stationary mhd; theorems stationary; type theorems; mhd equations ... See more keywords
New Liouville type theorems for the stationary Navier–Stokes, MHD, and Hall–MHD equations
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DOI: 10.1088/1361-6544/ad1efc
Abstract: We establish new Liouville-type theorems for weak solutions of the stationary Navier–Stokes equations, stationary magnetohydrodynamics (MHD) equations and stationary Hall–MHD equations under some conditions on the growth of certain Lebesgue norms of the velocity and… read more here.
Keywords: navier stokes; mhd equations; type theorems; liouville type ... See more keywords
Error Analysis of a PFEM Based on the Euler Semi-Implicit Scheme for the Unsteady MHD Equations
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DOI: 10.3390/e24101395
Abstract: In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “∇·u=0”, which… read more here.
Keywords: euler semi; mhd equations; pfem; semi implicit ... See more keywords