相关论文: A class large solution of the 3D Hall-magnetohydro…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
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…
In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is…
This paper is devoted to the study of relativistic Vlasov-Maxwell system in three space dimension. For a class of large initial data, we prove the global existence of classical solution with sharp decay estimate. The initial Maxwell field…
We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence…
This article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions.…
This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber…
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…
Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and…
The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
In this paper, the 3-D compressible MHD equations with initial vacuum or infinity electric conductivity is considered. We prove that the $L^\infty$ norms of the deformation tensor $D(u)$ and the absolute temperature $\theta$ control the…
Here we establish a global well-posedness of \textit{mild} solutions to the three-dimensional incompressible Navier-Stokes equations if the initial data are in the space $\mathcal{X}^{-1}$ defined by $(1.3)$ and if the norms of the initial…
Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the…
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…
The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…
In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $\chi^{-1}(\mathbb{R}^2)$ with any initial data in…
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…