In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to
form strong current sheets on their edges. Associated with these current sheets are magnetic …

In this paper, a second-order finite volume Non-Homogeneous Riemann Solver is used to
obtain an approximate solution for the two-dimensional shallow water …

We examine a frictional effect on the linear stability of an interface of discontinuity in
tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the …

We study the structural stability of shock waves and current-vortex sheets in shallow water
magnetohydrodynamics (SMHD) in the sense of the local-in-time existence and uniqueness …

In this paper, we derive new shallow asymptotic models for the free boundary plasma-
vacuum problem governed by the magnetohydrodynamic equations which are vital when …

We investigate an initial-boundary value problem for the one-dimensional rotating shallow
water magnetohydrodynamic equations. The Dirichlet boundary conditions are imposed …

Magnetohydrodynamic rotating shallow water system (MRSW) is a proposed model for a
thin layer of electrically conducting fluid, which plays an important role in astrophysical …

It is well known that an interface of tangential velocity discontinuity is necessarily unstable,
regardless of the velocity difference's strength, so-called the Kelvin-Helmholtz instability …

In this paper, the instability of shallow-water shear flow with a sheared parallel magnetic
field is studied. Waves propagating in such magnetic shear flows encounter critical levels …

The hydrodynamic instability of variable density swirling flows under gravity between two
infinite coaxial cylinders is investigated for axisymmetric disturbances. It is shown that the …