LOCAL EXISTENCE AND BLOW-UP CRITERION OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS

We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.

REGULARITY CRITERIA FOR WEAK SOLUTION TO THE 3D MAGNETOHYDRODYNAMIC EQUATIONS

In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS

We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.

Galerkin-Petrov least squares mixed element method for stationary incompressible magnetohydrodynamics

The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.

A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic （MHD） equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations axe directly constructed.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.

Regularization by transport noises for 3D MHD equations

We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data with high probability.

Formation of Singularity for Full Compressible Magnetohydrodynamic Equations with Zero Resistivity in Two Dimensional Bounded Domains

We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.

Regularity Criteria of the Magnetohydrodynamic Equations in a Bounded Domain

Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.

Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations

In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.

Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data

In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.

Existence of Weak Solutions to the Three-dimensional Steady Compressible Magnetohydrodynamic Equations

The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.

MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations.It turns out to be robust for relatively large physical parameters.By extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.

Global Well-posedness of the Non-isentropic Full Compressible Magnetohydrodynamic Equations

In this paper, we are concerned with Cuuchy problem for the multi-dimensional （N 〉_ 3） non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and unique- ness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms.

Global Helically Symmetric Solutions to 3D MHD Equations

We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.

The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows

In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The difference between the one-dimensional and multi-dimensional cases is a feature for compressible flows and also brings new difficulties. In contrast to the multi-dimensional case, the decay rates of nonlinear terms may not be faster than linear terms in dimension one. To handle this, we shall present a new energy estimate in terms of a combination of the solutions with small initial data. We aim to establish the sharp upper and lower bounds on the L^(2)-decay rates of the solutions and all their spatial derivatives when the initial perturbation is small in L^(1)(R) ∩ H^(2)(R). It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solutions so that the large-time behavior for the hyperbolic-parabolic system is exactly sharp. As a byproduct, the above result is also valid for compressible Navier-Stokes equations. Our approach is based on various interpolation inequalities, energy estimates, spectral analysis, and Fourier time-splitting and high-low frequency decomposition methods.

Plasma Edge Kinetic-MHD Modeling in Tokamaks Using Kepler Workflow for Code Coupling,Data Management and Visualization

A new predictive computer simulation tool targeting the development of the H-mode pedestal at the plasma edge in tokamaks and the triggering and dynamics of edge localizedmodes(ELMs)is presented in this report.This tool brings together,in a coordinated and effective manner,several first-principles physics simulation codes,stability analysis packages,and data processing and visualization tools.A Kepler workflow is used in order to carry out an edge plasma simulation that loosely couples the kinetic code,XGC0,with an ideal MHD linear stability analysis code,ELITE,and an extended MHD initial value code such as M3D or NIMROD.XGC0 includes the neoclassical ion-electron-neutral dynamics needed to simulate pedestal growth near the separatrix.The Kepler workflow processes the XGC0 simulation results into simple images that can be selected and displayed via the Dashboard,a monitoring tool implemented in AJAX allowing the scientist to track computational resources,examine running and archived jobs,and view key physics data,all within a standard Web browser.The XGC0 simulation is monitored for the conditions needed to trigger an ELM crash by periodically assessing the edge plasma pressure and current density profiles using the ELITE code.If an ELM crash is triggered,the Kepler workflow launches the M3D code on a moderate-size Opteron cluster to simulate the nonlinear ELM crash and to compute the relaxation of plasma profiles after the crash.This process is monitored through periodic outputs of plasma fluid quantities that are automatically visualized with AVS/Express and may be displayed on the Dashboard.Finally,the Kepler workflow archives all data outputs and processed images using HPSS,as well as provenance information about the software and hardware used to create the simulation.The complete process of preparing,executing and monitoring a coupled-code simulation of the edge pressure pedestal buildup and the ELM cycle using the Kepler scientific workflow system is described in this paper.