相关论文: Global regularity of logarithmically supercritical…

In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: $u_0=u_0^r e_r+\ut_0 e_\theta+u_0^z e_z, ~b_0=b_0^\theta e_\theta.$ We prove that, this system is global well-posed…

In this article, we consider the Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations…

In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in $\mathbb{R}^3$. This result is analogous to the celebrated…

\large{\bf Abstract-} Unsteady Hall Magnetohydrodynamics (MHD) near a hyperbolic magnetic neutral line is investigated. An exact analytical solution describing a self-similar evolution is given. This solution shows a negligible impact on…

We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the magnetic helicity precisely equals the initial magnetic…

In this paper, we investigate the characteristic structure of the full equations of magnetohydrodynamics (MHD) and show that it satisfies the hypotheses of a general variable-multiplicity stability frame- work introduced by Metivier and…

In this paper we study the global regularity for the solution to the Dirichlet problem of the equation of minimal graphs over a convex domain in hyperbolic spaces. We find that the global regularity depends only on the convexity of the…

In this paper we consider three-dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving…

We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole three-dimensional space and they consider the action of external forces. The first system deals with the simplified…

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…

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary…

We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary…

In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…

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…

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy…

We study the stochastic Nonlinear Schr\"{o}dinger system with multiplicative white noise in energy space $H^1$. Based on deterministic and stochastic Strichartz estimates, we prove the local well-posedness and uniqueness of mild solution.…

The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric…

This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when $\alpha+\beta=1+\frac{n}{2}$ satisfying…

We establish global well-posedness of strong solutions for the nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and initial density allowing vanish in two-dimensional (2D) bounded domains. Applying delicate…

We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine…