3D Incompressible MHD Research Articles

A Generalized Blow up Criteria with One Component of Velocity for 3D Incompressible MHD System

A Generalized Blow up Criteria with One Component of Velocity for 3D Incompressible MHD System

Optimal error analysis of an unconditionally stable BDF2 finite element approximation for the 3D incompressible MHD equations with variable density

This paper presents a second-order finite element scheme for the approximations of the three-dimensional (3D) incompressible magnetohydrodynamics system with variable density (VD-MHD), where two-step backward differentiation formula (BDF2) is used to discrete the time derivative and the (P2,P1b,P1,P1) finite elements are used to approximate the density, velocity, pressure and magnetic. Based on an equivalent VD-MHD system, the proposed finite element algorithm is unconditionally stable in the sense that the discrete energy inequalities hold without small condition of the time step size. After a rigorous analysis, the optimal L2 error estimates (τ2+h2) of the density, velocity field and magnetic field are established, where τ and h are the time step size and mesh size. Finally, numerical results are given to support these convergence rates.

三维不可压MHD方程在变指数Lebesgue空间中的适定性

三维不可压MHD方程在变指数Lebesgue空间中的适定性

Regularity criteria for the 3D axisymmetric non-resistive MHD system

The main purpose of this paper is to study regularity criteria for a class of axisymmetric solutions to 3D incompressible non-resistive MHD system. We establish that strong solutions of this system can be smoothly extended beyond the possible blow-up time T if the horizontal angular component of the velocity in some mixed Lorentz spaces. Our result extends and generalizes the corresponding result of Wang and Guo.

Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (∂1u1,∂1b1), (∂2u2,∂2b2) and (∂3u3,∂3b3) in anisotropic Lorentz space.

On regularity of the 3D MHD equations based on one velocity component in anisotropic Lebesgue spaces

In this paper we establish a new regularity criterion for the 3D incompressible MHD equations via ∂3u3 and the magnetic field b. By considering different weights in spatial variables, we show in anisotropic Lebesgue spaces if ∂3u3 and b satisfy certain space–time integrable conditions, which are almost optimal from the scaling invariant point of view, then a weak solution (u,b) is actually regular. This result gives new insights into the understanding of regularity theory of weak solutions.

An optimal regularity criterion for the 3D MHD equations in homogeneous Besov spaces

In this paper, we establish a new regularity criterion for weak solutions to the 3D incompressible MHD equations in terms of two pairs of (∂iui, ∂ibi) . More precisely, it is proved that the weak solution (u, b) is smooth on (0, T], provided that for some i, j ∈ {1, 2, 3} with i ≠ j, it holds that

Global well-posedness and decay characterization of solutions to 3D MHD equations with Hall and ion-slip effects

In this paper, we establish a small data global well-posedness results for 3D incompressible MHD equations with Hall and ion-slip effects. Then, by using Fourier splitting method and iteration, we consider the decay rate on higher order derivative of solutions.

Global solutions to 3D incompressible rotational MHD system

This study investigates the Cauchy problem of an incompressible magnetohydrodynamic system in the rotational framework. Under the assumption that the rotation speed is sufficiently large, the Cauchy problem is shown to be globally well-posed in $$H^{s}({{\mathbb {R}}}^3)\times (L^2\cap L^q) ({{\mathbb {R}}}^3)$$ for $$\frac{1}{2}<s < \frac{3}{4}$$ and $$3<q < \min \{\frac{6}{3-2s},\,\frac{27}{6 + 4s}\}$$ .

Long time behavior of solutions to 3D generalized MHD equations

Abstract In this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian. Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space ℝ 3 {\mathbb{R}^{3}} , we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy α , β ∈ ( 0 , 2 ] {\alpha,\beta\in(0,2]} .

Global stability of large solutions to the 3D nonhomogeneous incompressible MHD equations

In this paper, we consider the 3D nonhomogeneous incompressible MHD equations. More precisely, we obtain that the large solutions to the 3D nonhomogeneous incompressible MHD equations in 3D bounded or unbounded domains are stable under the conditions, where the initial data satisfy small perturbations and the suitable condition is prescribed on the large solutions.

Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system

In this work, we study the regularity criterion for the 3D incompressible MHD equations. By making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one component of the velocity vector field, both in scaling invariant spaces. Moreover, the norms imposed on the magnetic vector field are the Lebesgue and anisotropic Lebesgue norms. This improved the result of our previous blow up criterion in [ 15 ], in which the magnetic vector field is bounded in critical Sobolev spaces.

The Energy Conservations and Lower Bounds for Possible Singular Solutions to the 3D Incompressible MHD Equations

In this note, we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations. Moreover, we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.

Magnetic effects in rotating flow of an Oldroyd-B fluid with chemical reaction and convective surface

Here, we have investigated 3D incompressible steady MHD flow of Oldroyd-B material in a rotating frame. The flow is caused through linearly stretched sheet. Applied magnetic field is accounted. Cubic autocatalytic chemical reaction is considered at the surface. Convective conditions at the boundary are considered for heat transport. Flow problem is modeled with the help of boundary layer approximations. Homotopy method is utilized for the series solutions. Impacts of physical variable are interpreted graphically. Heat transfer rate is presented in tabulated form.

A new regularity criterion for the 3D incompressible MHD equations via partial derivatives

We consider the regularity criterion for the incompressible MHD equations. We show that the weak solution is regular, provided that(0.1)(∂3w+,∂3w−)∈L5r4r−6(0,T;Lr(R3)) with 4≤r≤∞, or(0.2)(∂3w+,∂3w−)∈L11r7r−12(0,T;Lr(R3)) with 52≤r≤4.

On the critical blow up criterion with one velocity component for 3D incompressible MHD system

This work establishes a sharp regularity criterion for the 3D incompressible MHD equations. Let (v,b) be a smooth enough solution of the MHD system. In Liu (2016), Y. Liu proved the regularity of (v,b) on (0,T∗] if there exists p∈(4,∞) such that ∫0T∗(‖v3(t)‖Ḣ12+2pp+‖b(t)‖Ḣ12+2pp)dt<∞. In this article, we settle the case p∈[2,4] and our proof also works for the case p∈(4,∞).

Global existence and exponential decay of strong solutions for the 3D incompressible MHD equations with density-dependent viscosity coefficient

This paper deals with the 3D incompressible MHD equations with density-dependent viscosity in bounded domain. The global well-posedness of strong solutions is established in the vacuum cases, provided the assumption that $${\bar{\rho }}+\Vert H_0\Vert _{L^3}$$ is suitably small with large velocity, which extends the recent work (Song in Z Angew Math Phys 69(2):23, 2018) to the global one. Furthermore, the exponential decay of the solution is also obtained.

On Regularity for the 3D MHD Equations via One Directional Derivative of the Pressure

This work establishes a new regularity criterion for the 3D incompressible MHD equations in term of one directional derivative of the pressure (i.e., \(\partial _{3}P\)) on framework of the anisotropic Lebesgue spaces. More precisely, it is proved that for \(T>0\), if \(\partial _{3}P\in L^{\beta }(0,T; L^{\alpha }(\mathbb {R}^{2}_{x_{1}x_{2}};L^{\gamma }(\mathbb {R}_{x_{3}})))\) with \(\frac{2}{\beta }+\frac{1}{\gamma }+\frac{2}{\alpha }=k\in [2,3)\) and \(\frac{3}{k}\le \gamma \le \alpha \le \frac{1}{k-2},\) then the corresponding solution (u, b) to the 3D MHD equations is regular on [0, T].

Global strong solutions to the 3D incompressible MHD equations with density-dependent viscosity

This paper is concerned with the 3D incompressible MHD equations with density-dependent viscosity in smooth bounded domains. Through time-weighted a priori estimates, the global existence of strong solutions is established under the assumption that the initial energy is suitably small. This generalizes previous results for the 3D Navier–Stokes equations in Huang and Wang (2015) and Zhang (2015), which need ‖∇u0‖L2 to be small. The initial vacuum is allowed.

Low Mach number limit for a model of accretion disk

We study an hydrodynamical model describing the motion of thick astrophysical disks relying on compressible Navier-Stokes-Fourier-Poisson system. We also suppose that the medium is electrically charged and we include energy exchanges through radiative transfer. Supposing that the system is rotating, we study the singular limit of the system when the Mach number, the Alfven number and Froude number go to zero and we prove convergence to a 3D incompressible MHD system with radiation with two stationary linear transport equations for transport of radiation intensity.