Related papers: New tests for a singularity of ideal MHD
The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field.…
We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr\"odinger map with values on the…
It has been known since work of Lichtenstein [42] and Gunther [29] in the 1920's that the $3D$ incompressible Euler equation is locally well-posed in the class of velocity fields with H\"older continuous gradient and suitable decay at…
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux…
We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for…
We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…
By performing estimates on the integral of the absolute value of vorticity along a local vortex line segment, we establish a relatively sharp dynamic growth estimate of maximum vorticity under some assumptions on the local geometric…
Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the structure constants of the Lie algebra {\it sdiff}$(T^2)$ of the group of area-preserving diffeomorphisms of a 2D torus. Thus Zeitlin and…
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded…
We consider 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. It describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. A local existence…
For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data. This is so despite great advances over…
Compressible ideal magnetohydrodynamics (MHD) is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic…
We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in…
We study the three-dimensional incompressible magnetohydrodynamic (MHD) equations near Couette flow with a constant magnetic field perpendicular to the shear plane. Couette flow induces mixing and generates magnetic induction, while the…
We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In…
We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector rather than the velocity. It enables a feasible Lagrangian study of fluid dynamics, as the isosurface of…
We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536^3 points and up to Taylor Reynolds number of 1200. The initial conditions are such that the…
The MOdified Newtonian Dynamics (MOND) is an alternative to the dark matter assumption that can explain the observed flat rotation curve of galaxies. Here hydrodynamic accretion is considered to critically check the consistency and to…
In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed…
We describe a new method to include magnetic fields into smooth particle hydrodynamics. The derivation of the self-gravitating hydrodynamics equations from a variational principle is discussed in some detail. The non-dissipative magnetic…