Related papers: Remarks on the global regularity of two-dimensiona…
In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…
We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling…
We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the magnetic helicity precisely equals the initial magnetic…
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…
The GENERIC structure allows for a unified treatment of different discrete models of hydrodynamics. We first propose a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We…
We construct self-adjoint Laplacians and symmetric Markov semigroups on hyperbolic attractors, endowed with Gibbs $u$-measures. If the measure has full support, we can also conclude the existence of an associated symmetric diffusion…
The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…
The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
Using a combined analytical/molecular dynamics (MD) approach, we study the current fluctuation spectra and longitudinal and transverse collective mode dispersions of the classical two-dimensional (point) dipole system (2DDS) characterized…
This work investigates the existence and uniqueness of local weak solutions for the d-dimensional $(d \geq 2)$ fractional magnetic B\'enard system without thermal diffusion, integrating the B\'enard equation and MHD system. For $\kappa = 0$…
We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the…
We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the…
At the zero temperature limit, a one-dimensional steady solution to the hydrodynamic equation of a U(2) invariant superfluid is obtained. This solution reveals that the magnitude of magnetization is always directly proportional to the…
Recent experiments have elucidated that novel nonequilibrium states inherent in the so-called hydrodynamic regime are realized in ultrapure metals with sufficiently strong momentum-conserving scattering. In this letter, we formulate a…
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of…
A good compromise between the resistive model and the PIC model is Aristotelian electrodynamics, which can include the back-reaction of the radiative photons onto particle motion and allow for a local dissipation where the force-free…
This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to…