Related papers: The magneto-geostrophic equations: a survey
In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields…
We prove the global existence of classical solutions to a class of forced drift-diffusion equations with $L^2$ initial data and divergence free drift velocity $\{u^\nu\}_{\nu_\ge0}\subset L^\infty_t BMO^{-1}_x$, and we obtain strong…
We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary…
We demonstrate that the 1D cylindrical version of the Grad-Shafranov equation is more rich than classical self-similar ones, and more suitable for the astrophysical jets we observe. In particular, it allows us to describe the central (and,…
Turbulence in rotating Magneto-hydrodynamic systems is studied theoretically and numerically. In the linear limit, when the velocity and magnetic perturbations are small, the system supports two types of waves. When the rotation effects are…
The dynamics contained in magnetized layers of exoplanet atmospheres are important to understand in order to characterize what observational signatures they may provide for future observations. It is important to develop a framework to…
A set of equations describing the rotational motion of the Earth relative to the GCRS is formulated in the approximation of rigidly rotating multipoles. The external bodies are supposed to be mass monopoles. The derived set of formulas is…
We present three-dimensional force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad-Shafranov equation. This result indicates…
A new magnetization equation recently derived from irreversible thermodynamics is employed to the calculation of an increase of ferrofluid viscosity in a magnetic field. Results of the calculations are compared with those obtained on the…
We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the…
The structure of geomagnetism is very complex, and there are still some problems left in magnetohydrodynamics (MHD) simulations. Recently, the macro spin model has been suggested. This is the idea that geomagnetism is described by…
This paper is a continuation and an extension of our recent work [13] on the identification of magnetized anomalies using geomagnetic monitoring, which aims to establish a rigorous mathematical theory for the geomagnetic detection…
It is usually believed that the geo-dynamo of the Earth or more generally of other planets, is created by the convective fluid motions inside their molten cores. An alternative to this thermal or compositional convection can however be…
One of the most intriguing features of Earth's axial magnetic dipole field, well-known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the…
We propose an exact solution for a stratosphere dynamical core formulated in geopotential/pressure coordinates with a time-evolving lower boundary supplied by the troposphere. Rather than constraining the stratospheric circulation via…
We review the main properties of shell models for magnetohydrodynamic (MHD) turbulence. After a brief account on shell models with nearest neighbour interactions, the paper focuses on the most recent results concerning dynamical properties…
A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…
The swept-field experiments on magnetic molecular solids such as \Fe8 are studied using Monte Carlo simulations. A kinetic equation is developed to understand the phenomenon. It is found that the simulations provide a quantitatively…
Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example.…
In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and…