Axisymmetric weak solutions to stationary compressible Navier-Stokes equations with critical indices

Abstract

This paper studies the isothermal stationary compressible Navier-Stokes equations on global space and cylinder domains. There are two critical exponents in such settings: The heat ratio 1 is an end point of the classical theory on weak solutions; the axisymmetric solutions in the global domain involve the critical index of Sobolev's inequality. Some new observations based on the cancellation structure of the equations are collected to get over these obstacles due to critical exponents.