Related papers: Approximate current-vortex sheets near the onset o…
We study the structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics (SMHD) in the sense of the local-in-time existence and uniqueness of discontinuous solutions satisfying corresponding jump…
We consider a 2D incompressible and electrically conducting fluid in the domain $\mathbb{T}\times\mathbb{R}$. The aim is to quantify stability properties of the Couette flow $(y,0)$ with a constant homogenous magnetic field $(\beta,0)$ when…
In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…
We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a symmetric system for the vector of primitive…
We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to…
We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…
We are concerned with the vortex sheet solutions for the inviscid two-phase flow in two dimensions. In particular, the nonlinear stability and existence of compressible vortex sheet solutions under small perturbations are established by…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
We consider the dynamics of a vortex sheet that evolves by the Birkhoff-Rott equations. The fluid evolution is understood as a weak solution of the incompressible Euler equations where the vorticity is given by a delta function on a curve…
A theory of the macroturbulent instability in the system containing vortices of opposite directions (vortices and antivortices) in hard superconductors is proposed. The origin of the instability is connected with the anisotropy of the…
We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape…
This paper studies the instability of two-dimensional magnetohydrodynamic (MHD) systems on a sphere using analytical methods. The underlying flow consists of a zonal differential rotation and a toroidal magnetic field is present. Semicircle…
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation…
\large{\bf Abstract-} Unsteady Hall Magnetohydrodynamics (MHD) near a hyperbolic magnetic neutral line is investigated. An exact analytical solution describing a self-similar evolution is given. This solution shows a negligible impact on…
In this paper, we address the problem of current-vortex sheets in ideal incompressible magnetohydrodynamics. More precisely, we prove a local-in-time existence and uniqueness result for analytic initial data using a Cauchy-Kowalevskaya…
We are concerned with the nonlinear stability of vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. This is a nonlinear hyperbolic problem with a characteristic free boundary. In this paper, we…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
The magnetohydrodynamic stability of axially unbounded cylindrical flows is considered which contain a toroidal magnetic background field with the same radial profile as the linear azimuthal velocity. Chandrasekhar (1956) has shown for…
In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The…