Related papers: On the Dynamical Stability and Instability of Park…
I consider the problem of weakly nonlinear stability of three-dimensional parity-invariant magnetohydrodynamic systems to perturbations, involving large scales. I assume that the MHD state, the stability of which I investigate, does not…
It is still an open problem whether the inhibition phenomenon of Rayleigh--Taylor (RT) instability by horizontal magnetic field can be mathematically proved in a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D)…
Motivated by the possibility of radiation driven instabilities in rotating magnetic stars, we study the stability properties of general linear perturbations of a stationary and axisymmetric, infinitely conducting perfect fluid configuration…
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary condition on velocity field and perfectly conducting wall…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides…
We analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasma screw pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration,…
We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of ${\mathbb {R}}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state…
In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly…
We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to…
It is still open whether the phenomenon of inhibition of Rayleigh--Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive \emph{viscous} magnetohydrodynamic (MHD) fluid in a two-dimensional…
We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a non-zero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set…
We investigate why the non-slip boundary condition for the velocity, imposed in the direction of impressed magnetic fields, can contribute to the magnetic inhibition effect based on the nonhomogeneous magnetic Rayleigh--Taylor (abbr. NMRT)…
We describe the effects of both magnetic buoyancy and differential rotation on a disc of isothermal gas embedded in a purely azimuthal magnetic field, in order to study the evolution and interplay of Parker and shearing instabilities. Both…
If a magnetic field normal to the surface of a magnetic fluid is increased beyond a critical value a spontaneous deformation of the surface arises (normal field instability). The instability is subcritical and leads to peaks of a…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
Parker instability leads to the formation of tangential discontinuities in a magnetic field and subsequent magnetic reconnection due to a numerical and/or an explicit resistivity. In this paper we investigate the role of the uniform,…
This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain perturbation problem. We find that the stability holds when…