Related papers: Asymptotic stability for $n$-dimensional isentropi…
We address the compressible magnetohydrodynamics (MHD) equations in $\mathbb{R}^3$ and establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum ($\rho= 0$) and the…
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $- \nu (- \triangle)^{\alpha} u$ and $- \kappa (-\triangle)^{\beta} b$. We show that smooth…
We analyze a two dimensional viscoresistive magnetohydrodynamical (MHD) model for a thin accretion disk which reconciles the crystalline structure outlined in [Coppi(2005), Coppi and Rousseau(2006)] with real microscopic and macroscopic…
We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular…
The three-wave resonant interaction (three-wave) equation not only possesses $3\times 3$ matrix spectral problem, but also being absence of stationary phase points, which give rise to difficulty on the asymptotic analysis with stationary…
The aim of this paper is to develop a stability theory and a numerical model for the three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full 3d problem to the shallow layer…
We study the three-dimensional Electron Magnetohydrodynamics (EMHD) equations without resistivity, a regime known to be ill-posed in Sobolev and Gevrey spaces due to the quasilinear nature of the system. Motivated by recent work on…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A major result of this paper establishes the global…
We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…
We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a…
We study the non-autonomous version of an infinite-dimensional port-Hamiltonian system on an interval $[a, b]$. Employing abstract results on evolution families, we show $C^1$-well-posedness of the corresponding Cauchy problem, and thereby…
The nonhomogeneous incompressible Magnetohydrodynamic Equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with slip boundary conditions. The key is the constraint of an additional initial value…
We deal with the barotropic compressible magnetohydrodynamic equations in three-dimensional (3D) bounded domain with slip boundary condition and vacuum. By a series of a priori estimates, especially the boundary estimates, we prove the…
We investigate the asymptotic stability of a tropical climate model posed on $\bR^2$, with temperature-dependent diffusion in the barotropic mode $u$ and linear damping in the first baroclinic mode $v$. We consider two distinct cases for…
In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity $\nu$, when the initial data is close to stable monotone shear flows.…
The local existence of smooth solutions to the inviscid Hall-MHD system has been obtained since Chae, Degond and Liu [Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, {31} (2014), 555--565]. However, as we known, how to construct the global…
We present steady-state solutions for a one-dimensional, magnetically-driven accretion disk wind model based on magnetohydrodynamic equations. We assume a geometrically thin, gas-pressure-dominated accretion disk, incorporating both…
This paper aims to numerically verify the large Reynolds number asymptotic theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper Deguchi (2019). To avoid any complexity associated with the chaotic nature of turbulence…
In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $\mathbb{T}\times \mathbb{R}$. In the inviscid case there is a generic…