Related papers: Weak stability of the plasma-vacuum interface prob…
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…
It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to…
We establish the local existence and uniqueness of multi-dimensional contact discontinuities for the ideal compressible magnetohydrodynamics (MHD) in Sobolev spaces, which are most typical interfacial waves for astrophysical plasmas and…
We study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics (MHD). They are characteristic discontinuities with no flow across the discontinuity for which the pressure, the magnetic field and…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…
Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…
This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…
Starting from a simple marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become…
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 investigate the linear stability properties of the plane interface separating two relativistic magnetized flows in relative motion. The two flows are governed by the (special) relativistic equations for a magnetized perfect gas in the…
We consider a free boundary problem for the incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. The magnetic field is tangent and the total pressure vanishes along the plasma-vacuum…
Compressible vortex sheets are fundamental waves in entropy solutions to the multidimensional hyperbolic systems of conservation laws. For the Euler equations in 2-D gas dynamics, the classical linearized stability analysis on compressible…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
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…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. In this work, the setting is two and…
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…
We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincar\'e…