Related papers: Discretely self-similar solutions for electron MHD
We study several types of self-similar solutions for the electron magnetohydrodynamics (MHD) without resistivity, including locally self-similar solutions and pseudo-self-similar solutions. We show that under certain conditions, these types…
We consider the electron magnetohydrodynamics (MHD) equation on the 3D torus $\mathbb T^3$. For a given smooth vector field $H$ with zero mean and zero divergence, we can construct a weak solution $B$ to the electron MHD in the space…
Via convex integration, we construct weak solutions to the non-resistive electron-MHD system which do not conserve energy and magnetic helicity.
We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot…
The electron magnetohydrodynamics (MHD) contains a highly nonlinear Hall term with an interesting structure. Exploring the Hall nonlinear structure, we investigate possible phenomena of finite time blow up for the electron MHD with a…
We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in $\Bbb R^n$, $n=2,3$, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic…
We consider the electron magnetohydrodynamics (MHD) with static background ion flow. A special situation of $B(x,y,t)=\nabla\times (a\vec e_z)+b \vec e_z$ with scalar-valued functions $a(x,y,t)$ and $b(x,y,t)$ was studied numerically in the…
This paper concerns with the explicit blowup phenomenon for 3D incompressible MHD equations in R^3. More precisely, we find two family of explicit blowup solutions for 3D incompressible MHD equations in R^3. One family of solutions admit…
We prove the local wellposedness of the Cauchy problems for the electron magnetohydrodynamics equations (E-MHD) without resistivity for possibly large perturbations of nonzero uniform magnetic fields. While the local wellposedness problem…
We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which has a rich family of steady states. In an anisotropic resistivity context, we show global in time existence of small smooth solution near a shear type…
The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being…
In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar MHD for a non-rotating…
We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) in the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic…
The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field.…
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…
This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup…
In this paper we exclude the scenario of apparition of finite time singularity in the form of self-similar singularities in the ideal magnetohydrodynamic equations, assuming suitable integrability conditions on the vorticity and the…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
The equations of 2D incompressible dissipationless extended magnetohydrodynamics (XMHD) extend the equations of incompressible Hall MHD (HMHD) by retaining finite-electron inertia. These XMHD equations couple the fluid velocity ${\bf V} =…
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…