相关论文: Singularity formation for the incompressible Hall-…
In this paper, we first prove the local well-posedness of strong solutions to the incompressible Hall-MHD system for initial data $(u_0,B_0)\in H^{\frac{1}{2}+\sigma}(\mathbb{R}^3)\times H^{\frac{3}{2}}(\mathbb{R}^3)$ with $\sigma\in…
In this paper, we investigate the well-posedness and ill-posedness issues for the incompressible stationary Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{R}^3.$ We first show the existence and uniqueness of solutions provided with…
It has been shown in our previous work that the incompressible and irresistive Hall- and electron-magnetohydrodynamic (MHD) equations are illposed on flat domains $M = \mathbb{R}^k \times \mathbb{T}^{3-k}$ for $0 \le k \le 2$. The data and…
In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in $\mathbb{R}^3$. We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of…
We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first aim is to provide the reader with an elementary proof of a global well-posedness result for small data with critical Sobolev regularity, in…
In this paper, we prove a sharp ill-posedness result for the incompressible non-resistive MHD equations. In any dimension $d\ge 2$, we show the ill-posedness of the non-resistive MHD equations in $H^{\frac{d}{2}-1}(\mathbb{R}^d)\times…
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 consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global…
We show that the viscous resistive magneto-hydrodynamics system with Hall effect is locally well-posed in $H^s(\mathbb R^n)\times H^{s+1-\varepsilon}(\mathbb R^n)$ with $s>\frac{n}2-1$ and any small enough $\varepsilon>0$ such that…
In this paper, we study the local well-posedness of classical solutions to the ideal Hall-MHD equations whose magnetic field is supposed to be azimuthal in the $L^2$-based Sobolev spaces. By introducing a good unknown coupling with the…
Due to the singular nonlinear Hall term, the non-resistive electron magnetohydrodynamics (MHD) is not known to be locally well-posed in general. In this paper we consider the $2\frac12$D electron MHD with either horizontal or vertical…
We investigate the existence and uniqueness issues of the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial velocity $u_0$ and magnetic field $B_0$ in critical regularity spaces.In the case where $u_0,$ $B_0$ and…
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $…
In this paper, we study the global well-posedness of the incompressible Hall-MHD system for small initial data $( u_0, b_0) \in \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \times \Big( \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \cap \dot…
We study the problem of propagation of regularity of solutions to the incompressible viscous non-resistive magneto-hydrodynamics system. According to scaling, the Sobolev space $H^{\frac n2-1}(\mathbb R^n)\times H^{\frac n2}(\mathbb R^n)$…
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^d$, $d=2,3$, with initial data $B_0\in H^s(\mathbb{R}^d)$ and $u_0\in…
We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical…
In this paper, we study the singularity formation phenomenon of the 1D model of Electron Magnetohydrodynamics (EMHD). we will construct a solution whose $C^3$-norm blows up in finite time. In the end, we will show that the solution is in…
We consider the magnetohydrodynamics system with Hall effect accompanied with initial data in supercritical Sobolev space. Via an appropriate randomization of the supercritical initial data, both local and small data global well-posedness…
This paper characterizes the possible blow-up of solutions for the 3D magneto-hydrodynamics (MHD for short) equations. We first establish some $\epsilon$-regularity criteria in $L^{q,\infty}$ spaces for suitable weak solutions, and then…