Resistive tearing modes in a sheet pinch with shear flow

Resistive tearing modes are analysed in a plane sheet pinch with shear bulk plasma flow present. A perturbation theory using asymptotic series is applied for small resistivity and sero viscosity. The analyticity problems arising in the vicinity of singular points are taken into account. For a suitably defined solution uniform convergence is proved and the scaling law for the growth rate derived. The instability region is shown to depend on the function fluid kinetic energy magnetic field energy where both stabilization and destabilization are possible effect of the shear flow. The relationship to the Kelvin-Helmholtz instability is discussed.