SELF-SIMILAR ISOTHERMAL IRROTATIONAL MOTION FOR THE EULER, EULER–POISSON SYSTEMS AND THE FORMATION OF THE PLASMA SHEATH

We consider the self-similar dynamics of a compressible irrotational isothermal fluid and show that a variant of Elling–Liu's ellipticity principle holds. Specially we prove that a closed pseudo-Mach surface is inconsistent with smooth flow. Furthermore, we give an application of our result to the formulation of a plasma sheath in a plasma consisting of cold ions and hot electrons.