Related papers: Asymptotic shallow models arising in magnetohydrod…
We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its…
The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the…
We describe a new method to include magnetic fields into smooth particle hydrodynamics. The derivation of the self-gravitating hydrodynamics equations from a variational principle is discussed in some detail. The non-dissipative magnetic…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
Motivated by some models arising in quantum plasma dynamics, in this paper we study the Maxwell-Schr\"odinger system with a power-type nonlinearity. We show the local well-posedness in $H^2(\mathbb{R}^3)\times H^{3/2}(\mathbb{R}^3)$ and the…
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by…
We consider various sets of Vlasov-Fokker-Planck equations modeling the dynamics of charged particles in a plasma under the effect of a strong magnetic field. For each of them in a regime where the strength of the magnetic field is…
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white…
We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in…
Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for…
The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated…
How the turbulent energy cascade develops below the magnetohydrodynamic scales in space and astrophysical plasmas is a major open question. Here, we measure the power spectrum of magnetic fluctuations in Parker Solar Probe's observations…
The general-relativistic (GR) magnetohydrodynamic (MHD) equations for a conductive plasma fluid are derived and discussed in the curved spacetime described by Thorne's metric tensor, i.e., a family of cosmological models with inherent…
This letter discusses rotating magnetohydrodynamics (MHD) of a thin layer of astrophysical plasma. To describe a thin plasma layer with a free surface in a vertical external magnetic field we use the shallow water ap- proximation. The…
A fluid description for collisionless magnetized plasmas that takes into account the effect of cyclotron resonance has been developed. Following the same approach as the Landau fluid closure, the heat flux components associated with…
For the free boundary problem of the plasma-vacuum interface to ideal incompressible magnetohydrodynamics (MHD) in two-dimensional space, the a priori estimates of solutions are proved in Sobolev norms by adopting a geometrical point of…
Using $10,\!080^3$ grid simulations, we analyze scale-dependent alignment in driven, compressible, no net-flux magnetohydrodynamic turbulence. The plasma self-organizes into localized, strongly aligned regions. Alignment spans all primitive…
In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are…
For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of…
Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…