Full Compressible MHD Research Articles

Local well-posedness to the full compressible MHD equations without initial compatibility conditions

Local well-posedness to the full compressible MHD equations without initial compatibility conditions

Space–time decay rates for the 3D full compressible MHD equations

Space–time decay rates for the 3D full compressible MHD equations

Global well-posedness and exponential decay rates of the strong solutions to the two-dimensional full compressible magnetohydrodynamics equations with vacuum in some class of large initial data

In this paper, the initial-boundary value problem for the two-dimensional viscous, compressible, and heat conducting magnetohydrodynamics equations with vacuum is considered. When all the coefficients of viscosity, heat conductivity and magnetic diffusivity are constants, first, we show that for general initial data and any time T>0, the local strong solution in the sense of Sobolev norms will never blow-up provided that the density is bounded from above and the temperature belongs to space L∞(0,T;L2)∩L2(0,T;L∞). Second, based on the above blow-up criterion and the delicate analysis of the nonlinear strong coupling equations, we establish the global existence of strong solutions when the initial mass of the fluid and the initial energy of the magnetic field (i.e., ‖ρ0‖L1 and ‖H0‖L2) are suitably small, where the refined Zlotnik inequality and the decoupling of the full compressible MHD equations play an essential role in proving the uniform upper bound of the density and the higher-order a priori uniform in time estimates, respectively. It is worth mentioning that the initial velocity and temperature can be large. Moreover, we obtain exponential decay under the H1-norm of (u,θ,H) and L2-norm of (ρu˙,ρθ˙,Ht), where the long-time behaviors of the higher-order derivative of velocity are given and it is different from the known results.

Uniform regularity for the nonisentropic MHD system

In this work, we prove the uniform regularity of smooth solutions to the full compressible MHD system in \(\mathbb{T}^3\). Here our result is obtained by using the bilinear commutator and product estimates.

Global well-posedness and time-decay for the full compressible non-resistive MHD equations in a 3D infinite slab

This paper is concerned with the global well-posedness and time-decay of the system of full compressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no compatibility conditions on the initial data.

Optimal large-time behavior of the full 3D compressible MHD system

We investigate optimal large-time behavior for higher-order spatial derivatives of strong solutions to the 3D full compressible MHD system. More precisely, we employ low-frequency and high-frequency decomposition and delicate energy estimates to show that

Low Mach number limit of the full compressible mhd equations with Cattaneo’s heat transfer law

Low Mach number limit of the full compressible mhd equations with Cattaneo’s heat transfer law

A Regularity Criterion for the 2D Full Compressible MHD Equations with Zero Heat Conductivity

In this paper we establish a regularity criterion for the 2D full compressible MHD equations with zero heat conductivity and initial vacuum in a bounded domain.

Convergence from an electromagnetic fluid system to the full compressible MHD equations

We are concerned with the zero dielectric constant limit for the full electro-magneto-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 well-prepared 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.

Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition

In this paper, we consider the low Mach number limit of the full compressible MHD equations in a 3-D bounded domain with Dirichlet boundary condition for velocity field, Neumann boundary condition for temperature and perfectly conducting boundary condition for magnetic field. First, the uniform estimates in the Mach number for the strong solutions are obtained in a short time interval, provided that the initial density and temperature are close to the constant states. Then, we prove the solutions of the full compressible MHD equations converge to the isentropic incompressible MHD equations as the Mach number tends to zero.

Optimal decay rates of classical solutions for the full compressible MHD equations

In this paper, we are concerned with optimal decay rates for higher order spatial derivatives of classical solutions to the full compressible MHD equations in three dimensional whole space. If the initial perturbation are small in $H^3$-norm and bounded in $L^q(q\in \left[1, \frac{6}{5}\right))$-norm, we apply the Fourier splitting method by Schonbek[Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates for the second order spatial derivatives of solutions and the third order spatial derivatives of magnetic field in $L^2$-norm. These results improve the work of Pu and Guo [Z. Angew. Math. Phys. 64 (2013) 519-538].

Blowup of smooth solutions to the full compressible MHD system with compact density

This paper studies the blowup of smooth solutions to the full compressible MHD system with zero resistivity on $\mathbb{R}^{d}$, $d\geq 1$. We obtain that the smooth solutions to the MHD system will blow up in finite time, if the initial density is compactly supported.

Well-Posedness in Critical Spaces for the Full Compressible Mhd Equations

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in ℝN, N≥ 2 under the assumptions that the initial density is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.

Global existence and convergence rates of smooth solutions for the full compressible MHD equations

In this paper, we consider the global smooth solutions and their decay for the full compressible magnetohydrodynamic equations in R 3. We prove the global existence of smooth solutions near the constant state in Sobolev norms by energy method and show the convergence rates of the L p -norm of these solutions to the constant state when the L q -norm of the perturbation is bounded.

Observations and 3D MHD simulations of a solar active region jet

Aims. We study an active region jet originating from NOAA 8531 on May 15 1999. We perform 3D MHD numerical simulations of magnetic flux emergence and its subsequent reconnection with preexisting magnetic flux. Then, we compare the physical properties of the observed jet with the reconnecting outflow produced in the numerical model. Methods. We report observations of this jet using a series of TRACE 171 A filtergrams, simultaneous observations from SUMER in Ne viii 770A and C iv 1548 A as well as MDI magnetograms. In the numerical simulation, the full compressible and resistive MHD equations are solved, including viscous and Ohmic heating. Results. A high-velocity upflow ($\simeq$100 km s -1 ) is observed after the emergence of new magnetic flux at the edge of the active region. The jet is recorded over a range of temperatures between 10 5 K and $1.5 \times 10^6$ K. In our numerical experiments, we find that the jet is the result of magnetic reconnection between newly emerging flux and the preexisting magnetic field of the active region. Conclusions. The hot and high-velocity bidirectional flows occur as a result of the interaction between oppositely directed magnetic fields. Observations and numerical results are strongly suggestive of effective reconnection process being responsible for producing jets when emerging flux appears in solar active regions.

Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence

Direct numerical simulations of low Mach number compressible three-dimensional magnetohydrodynamic (CMHD3D) turbulence in the presence of a strong mean magnetic field are compared with simulations of reduced magnetohydrodynamics (RMHD). Periodic boundary conditions in the three spatial coordinates are considered. Different sets of initial conditions are chosen to explore the applicability of RMHD and to study how close the solution remains to the full compressible MHD solution as both freely evolve in time. In a first set, the initial state is prepared to satisfy the conditions assumed in the derivation of RMHD, namely, a strong mean magnetic field and plane-polarized fluctuations, varying weakly along the mean magnetic field. In those circumstances, simulations show that RMHD and CMHD3D evolve almost indistinguishably from one another. When some of the conditions are relaxed the agreement worsens but RMHD remains fairly close to CMHD3D, especially when the mean magnetic field is large enough. Moreover, the well-known spectral anisotropy effect promotes the dynamical attainment of the conditions for RMHD applicability. Global quantities (mean energies, mean-square current, and vorticity) and energy spectra from the two solutions are compared and point-to-point separation estimations are computed. The specific results shown here give support to the use of RMHD as a valid approximation of compressible MHD with a mean magnetic field under certain but quite practical conditions.

A conservative pressure‐correction method for the Euler and ideal MHD equations at all speeds

AbstractTo efficiently compute weakly compressible magnetohydrodynamic flows in astrophysical applications, approximate low Mach number reduced forms of the compressible MHD equations are frequently used. This is because standard characteristic‐based schemes for the full compressible MHD equations are inefficient and inaccurate for computing low Mach number magnetohydrodynamic flow, as a result of the increasing stiffness and weakening pressure/density coupling of the equations when M ↓ 0. Furthermore, these schemes are colocated, so that additional and artificial measures have to be taken to ensure solenoidality of the magnetic field. We present a new method with a staggered spatial discretization and a pressure‐correction solution algorithm that is more suitable for computing weakly compressible MHD flow, because of its Mach‐uniformity and efficient and accurate handling of the solenoidality constraint on the magnetic field. Copyright © 2002 John Wiley & Sons, Ltd.

Current profile flattening and hot core shift due to non-linear development of resistive kink mode

A new and interesting phenomenon that the toroidal current profile, which at first exhibits peaking due to ohmic heating, flattens around the magnetic axis is obtained through a full compressible resistive MHD simulation for a 3-D toroidal geometry. It is concluded that the current flattening is caused by non-linear excitation of the unstable m=1/n=1 resistive kink mode, specifically by the quasi-linear effect of the coupling of the plasma velocity and the magnetic field of the n=+or-1 mode. The time-scale of the current profile flattening is of the order of the MHD time-scale. When the current profile is largely flattened, the plasma dynamic pressure due to the strongly excited kink mode pushes the hot core plasma in the radial kink flow direction and the hot core starts deviating from the magnetic surface owing to the dynamic pressure and the plasma compressibility. Because of the reduction of the magnetic shear due to the current flattening in the q<1 region, magnetic field reconnection is driven by the strong kink flow and leads to the destruction of the magnetic field structure within the q=1 rational surface. Subsequently, the magnetic field configuration recovers to an axisymmetric profile. This can explain the fast crash phase of sawteeth in tokamaks. The effect of the thermal conduction on the evolution of such a process is also discussed