Related papers: Global Regularity of 2D Generalized MHD Equations …

In this paper, we study the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional bounded simply…

We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid $\alpha$-regularization of the three-dimensional Euler equations of ideal incompressible fluids. Moreover, we establish the…

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane $\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy method, we derive the local…

We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills the minimum entropy principle, and preserves the…

We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $\Lambda$-convex hull, the latter providing inequalities…

We are concerned with the uniform regularity estimates and vanishing viscosity limit of solution to two dimensional viscous compressible magnetohydrodynamics (MHD) equations with transverse background magnetic field. When the magnetic field…

In this paper, we consider a model for the spin-magnetization system that takes into account the diffusion process of the spin accumulation. This model consists of the Landau-Lifshitz equation describing the precession of the magnetization,…

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and…

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 will extend a recent result of B.~Choi and P.~Daskalopoulos (\cite{CD}). For any $n\ge 3$, $0<m<\frac{n-2}{n}$, $m\ne\frac{n-2}{n+2}$, $\beta>0$ and $\lambda>0$, we prove the higher order expansion of the radially symmetric solution…

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained…

The generalized general-relativisticmagnetohydrodynamic (generalized GRMHD) equations have been used to study specific relativistic-plasmas phenomena, such as relativistic magnetic reconnection or wave propagation modified by non-ideal MHD…

In this article we consider the following generalized quasi-geostrophic equation \partial_t\theta + u\cdot\nabla \theta + \nu \Lambda^\beta \theta =0, \quad u= \Lambda^\alpha \mathcal{R}^\bot\theta, \quad x\in\mathbb{R}^2, where $\nu>0$,…

This paper studies the global regularity problem for the 2D micropolar Rayleigh-B\'{e}nard convection system with velocity zero dissipation, micro-rotation velocity Laplace dissipation and temperature critical dissipation. By introducing a…

In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…

This paper aims to establish the global well-posedness of the free boundary problem for the incompressible viscous resistive magnetohydrodynamic (MHD) equations. Under the framework of Lagrangian coordinates, a unique global solution exists…

We prove global existence of strong solutions to the drift-diffusion-Maxwell system in two space dimension. We also provide an exponential growth estimate for the $H^1$ norm of the solution.

We prove global existence of a derivative bi-harmonic wave equation with a non-generic quadratic nonlinearity and small initial data in the scaling critical space $\dot{B}^{2,1}_{\frac{d}{2}}(\mathbb{R}^d) \times…

A recent generalisation of the Raychaudhuri equations for timelike geodesic congruences to families of $D$ dimensional extremal, timelike, Nambu--Goto surfaces embedded in an $N$ dimensional Lorentzian background is reviewed. Specialising…