Related papers: Vanishing shear viscosity and boundary layers for …
A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The…
Heat transport in quasi-static magnetoconvection with a vertical magnetic field in a plane layer geometry is investigated with direct numerical simulations and asymptotic theory in the limit of large Chandrasekhar number ($Q$). It is shown…
In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…
We consider the three-dimensional incompressible magnetohydrodynamics (MHD) equations in a bounded domain with small volume and free moving surface boundary. We establish a priori estimate for solutions with minimal regularity assumptions…
This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density…
The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space $\R^3$ and the three-dimensional periodic domains. The…
We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $\eta/s$.…
A shear flow of particles in a laser-driven two-dimensional (2D) dusty plasma are observed in a further study of viscous heating and thermal conduction. Video imaging and particle tracking yields particle velocity data, which we convert…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
The effect of non periodic boundary conditions on decaying two-dimensional magnetohydrodynamic turbulence is investigated. We consider a circular domain with no-slip boundary conditions for the velocity and where the normal component of the…
The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: $\alpha > 0$, corresponding to the elastic response, and $\nu > 0$, corresponding to viscosity. Formally setting these parameters to $0$ reduces the…
We study an initial boundary value problem for the 3D magnetohydrodynamics (MHD) equations of compressible fluids in $\R^3$. We establish a blow-up criterion for the local strong solutions in terms of the density and magnetic field. Namely,…
We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in…
We consider the initial-boundary value problem in the quarter space for the system of equations of ideal Magneto-Hydrodynamics for compressible fluids with perfectly conducting wall boundary conditions. On the two parts of the boundary the…
We study the three dimensional active scalar equation called the magneto-geostropic equation which was proposed by Moffatt and Loper as a model for the geodynamo processes in the Earth's fluid core. When the viscosity of the fluid is…
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…
This paper is concerned with a non-isentropic compressible Navier-Stokes/Allen-Cahn system with phase variable dependent viscosity $\eta(\chi)=\chi^\alpha$ and temperature dependent heat-conductivity $\kappa(\theta)=\theta^\beta$. We show…
We construct self-similar inflow-outflow solutions for a hot viscous-resistive accretion flow with large scale magnetic fields that have odd symmetry with respect to the equatorial plane in $B_\theta$, and even symmetry in $B_r$ and…
For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…
Historically, meteorological and climate studies have been prompted by the need for understanding precipitation to have better logistics in food production. Despite all efforts, nonlinearity in atmosphere dynamics is still a source of…