1,071 research outputs found
Initial value problem for the free boundary magnetohydrodynamics with zero magnetic boundary condition
We show local existence and uniqueness of plasma(fluid)-vaccum free boundary
problem of magnetohydrodynamic flow in three-dimensional space with infinite
depth setting when magnetic field is zero on the free boundary. We use
Sobolev-Slobodetskii space which was used in usual free boundary problem in
[3,5,6,7,8,9]. We also show that this solution can be extended as long as we
want for sufficiently small initial data. Using the result of this paper we
will get a unique solution of (kinematic inviscid) - (magnetic non diffusive)
free boundary magnetohydrodynamics problem via (kinematic viscosity) -
(magnetic diffusivity) limit in [10].Comment: Accepted in Comm. Math. Sci. (2017
Toroidal Vortices in Resistive Magnetohydrodynamic Equilibria
Resistive steady states in toroidal magnetohydrodynamics (MHD), where Ohm's
law must be taken into account, differ considerably from ideal ones. Only for
special (and probably unphysical) resistivity profiles can the Lorentz force,
in the static force-balance equation, be expressed as the gradient of a scalar
and thus cancel the gradient of a scalar pressure. In general, the Lorentz
force has a curl directed so as to generate toroidal vorticity. Here, we
calculate, for a collisional, highly viscous magnetofluid, the flows that are
required for an axisymmetric toroidal steady state, assuming uniform scalar
resistivity and viscosity. The flows originate from paired toroidal vortices
(in what might be called a ``double smoke ring'' configuration), and are
thought likely to be ubiquitous in the interior of toroidally driven
magnetofluids of this type. The existence of such vortices is conjectured to
characterize magnetofluids beyond the high-viscosity limit in which they are
readily calculable.Comment: 17 pages, 4 figure
Entropy-bounded solutions to the Cauchy problem of compressible planar non-resistive magnetohydrodynamics equations with far field vacuum
We investigate the Cauchy problem to the compressible planar non-resistive
magnetohydrodynamic equations with zero heat conduction. The global existence
of strong solutions to such a model has been established by Li and Li (J.
Differential Equations 316: 136--157, 2022). However, to our best knowledge, so
far there is no result on the behavior of the entropy near the vacuum region
for this model. The main novelty of this paper is to give a positive response
to this problem. More precisely, by a series of a priori estimates, especially
the singular type estimates, we show that the boundedness of the entropy can be
propagated up to any finite time provided that the initial vacuum presents only
at far fields with sufficiently slow decay of the initial density.Comment: 19 page
Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system
This paper deals with the derivation and analysis of the the Hall
Magneto-Hydrodynamic equations. We first provide a derivation of this system
from a two-fluids Euler-Maxwell system for electrons and ions, through a set of
scaling limits. We also propose a kinetic formulation for the Hall-MHD
equations which contains as fluid closure different variants of the Hall-MHD
model. Then, we prove the existence of global weak solutions for the
incompressible viscous resistive Hall-MHD model. We use the particular
structure of the Hall term which has zero contribution to the energy identity.
Finally, we discuss particular solutions in the form of axisymmetric purely
swirling magnetic fields and propose some regularization of the Hall equation
Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping
Diffferentially rotating stars can support significantly more mass in
equilibrium than nonrotating or uniformly rotating stars, according to general
relativity. The remnant of a binary neutron star merger may give rise to such a
``hypermassive'' object. While such a star may be dynamically stable against
gravitational collapse and bar formation, the radial stabilization due to
differential rotation is likely to be temporary. Magnetic braking and viscosity
combine to drive the star to uniform rotation, even if the seed magnetic field
and the viscosity are small. This process inevitably leads to delayed collapse,
which will be accompanied by a delayed gravitational wave burst and, possibly,
a gamma-ray burst. We provide a simple, Newtonian, MHD calculation of the
braking of differential rotation by magnetic fields and viscosity. The star is
idealized as a differentially rotating, infinite cylinder consisting of a
homogeneous, incompressible conducting gas. We solve analytically the simplest
case in which the gas has no viscosity and the star resides in an exterior
vacuum. We treat numerically cases in which the gas has internal viscosity and
the star is embedded in an exterior, low-density, conducting medium. Our
evolution calculations are presented to stimulate more realistic MHD
simulations in full 3+1 general relativity. They serve to identify some of the
key physical and numerical parameters, scaling behavior and competing
timescales that characterize this important process.Comment: 11 pages. To appear in ApJ (November 20, 2000
Theoretical Aspects of Blunt Body Magnetoaerodynamics
Supersonic magnetoaerodynamic flow about blunt body with self contained magnetic field sourc
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