Related papers: On the 2D Plasma-Vacuum Interface Problems for Ide…
We prove well-posedness for the 3-D compressible Euler equations with moving physical vacuum boundary, with an equation of state given by the so-called gamma gas-law for gamma > 1. The physical vacuum singularity requires the sound speed c…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
Fast reconnection in magnetically dominated plasmas is widely invoked in models of dissipation in pulsar winds, gamma-ray flares in the Crab nebula, and to explain the radio nanoshots of pulsars. When current sheets evolve reaching a…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, though the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$)…
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_0 \in H^{2.5+\delta }$ is such that $\mathrm{curl}\,u_0 \in H^{2+\delta }$ in an arbitrarily small neighborhood of…
A general stability condition for plasma-vacuum systems with resistive walls is derived by using the Frieman Rotenberg lagrangian stability formulation [Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit for…
We consider the three-dimensional incompressible magnetohydrodynamics (MHD) equations in a bounded domain with small volume and free moving surface boundary. We establish a priori estimate for solutions with minimal regularity assumptions…
In this paper, we present a new framework for the global well-posedness and large-time behavior of a two-phase flow system, which consists of the pressureless Euler equations and incompressible Navier-Stokes equations coupled through the…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments. We use a newly-developed Lagrangian relaxation scheme that…
In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields…
We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD "millenium simulation" of Passos & Charbonneau (2014). This simulation sustains a large-scale magnetic cycle characterized by solar-like…
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0,…
A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid"…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
For the system of cold plasma equations describing the motion of electrons in the field of stationary ions, we consider the Riemann problem posed at an impenetrable interface between two media. These media differ in the magnitude of the…
We provide a valid magnetohydrostatic equilibrium from the collapse of a 2D X-point in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, one-dimensional current…