Related papers: Approximate current-vortex sheets near the onset o…
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of…
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of…
The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal…
We are concerned with nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-boundary value problem with characteristic free boundary. It…
In this paper, we solve a long-standing open problem: nonlinear stability of current-vortex sheet in the ideal incompressible Magneto-Hydrodynamics under the linear stability condition. This result gives a first rigorous confirmation of the…
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…
This is the second part of the two-paper sequence, which aims to present a comprehensive study for current-vortex sheets in ideal compressible magnetohydrodynamics (MHD). The local well-posedness of current-vortex sheets with surface…
Current-vortex sheet is one of the characteristic discontinuities in ideal compressible magnetohydrodynamics (MHD). The motion of current-vortex sheets is described by a free-interface problem of two-phase MHD flows with magnetic fields…
We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions…
This work is devoted to the construction of weakly nonlinear, highly oscillating, current vortex sheet solutions to the incompressible magnetohydrodynamics equations. Current vortex sheets are piecewise smooth solutions to the…
This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…
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…
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…
This article considers the ideal 2D magnetohydrodynamic equations on an infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This setting combines important physical…
Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role for the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between…
We study the Rayleigh-Taylor problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows, with zero resistivity, surface tension (or without surface tenstion) and special initial magnetic field, evolving with a free…
This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the…
In the analysis of the long-time behaviour of two-dimensional incompressible viscous fluids, Oseen vortices play a major role as attractors of any homogeneous solution with integrable initial vorticity. As a first step in the study of the…
It is well known that the nonlinear evolution of magnetohydrodynamic (MHD) turbulence generates current sheets. In the solar wind turbulence, current sheets are frequently observed and they are believed to be an important pathway for the…