Remarks on classical solutions to steady quantum Navier-Stokes equations

Abstract

The paper of Dong [Dong, J. Classical solutions to one-dimensional stationary quantum Navier–Stokes equations, J. Math Pure Appl. 2011] which proved the existence of classical solutions to one-dimensional steady quantum Navier–Stokes equations, when the nonzero boundary value u0 satisfies some conditions. In this paper, we obtain a different version of existence theorem without restriction to u0. As a byproduct, we get the existence result of classical solutions to the stationary quantum Navier–Stokes equations.