Related papers: Existence and Stability of Compressible Current-Vo…
We study vortex patches for the 2D incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We instead consider the horizontally periodic setting. This…
The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative…
We revisit the 3D Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with vacuum as far field density. By delicate energy method, we derive global existence and uniqueness of strong solutions provided that…
We prove the local-in-time well-posedness for the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \fw) \in H^s\times H^s\times H^{s'}$, $2<s'<s$. The classical…
We find a new family of exact solutions of the Confined Vortex Surface equations (The Euler equations with extra boundary conditions coming from the stability of the Navier-Stokes equations in the local tangent plane). This family of…
We prove the existence of both local and global smooth solutions to the Cauchy problem in $\R^3$ for the incompressible magnetohydrodynamics (MHD) system. We also prove that the solution to the incompressible MHD system can be obtained as…
In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity…
This paper investigates the stabilization effect of a background magnetic vorticity on electrically conducting fluids. By exploring the dissipation nature of the linearized equations, we prove the global existence of smooth solutions to the…
Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfv\'{e}n waves, which interact and rapidly…
I construct a complete asymptotic expansion of solutions to the problem of linear stability of three-dimensional steady space-periodic magnetohydrodynamic states to perturbations involving large periods. Eddy diffusivity tensor is derived…
We investigate the stabilizing effects of the magnetic fields in the linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous incompressible viscous magnetohydrodynamic fluid of zero resistivity in the presence of a uniform…
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently…
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the…
Inertial effects in nonlinear magnetic reconnection are studied within the context of 2D electron magnetohydrodynamics (EMHD) with resistive and viscous dissipation. Families of nonlinear solutions for relevant current sheet parameters are…
We investigate the Kelvin-Helmholtz instability occuring at the interface of a shear flow configuration in 2D compressible magnetohydrodynamics (MHD). The linear growth and the subsequent non-linear saturation of the instability are studied…
It has been proposed recently by Loureiro & Boldyrev [Phys. Rev. Lett. 118, 245101 (2017)] and Mallet et al. [Mon. Not. R. Astron. Soc. 468, 4862 (2017)] that strongly anisotropic current sheets formed in the inertial range of…
Here, we investigate the linear spatial stability of a parallel two-dimensional compressible boundary layer on an adiabatic plate by considering 2D and 3D disturbances. We employ the Compound Matrix Method for the first time for…
We analyse numerically the linear stability of a liquid metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three dimensional vector stream…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…