On the static-limit solutions to the Navier-Stokes equations of compressible flow (Q5956418)

The author considers stationary compressible isentropic Navier-Stokes equations describing the distribution of fluid density in a spatial \(n\)-dimensional domain, assuming that the flow is driven by a time-independent external potential force. It is shown that there exists a critical fluid mass \(m_c\) such that the problem admits at most two solutions for \(m<m_c\) for each energy \(e\in\mathbb{R}\), and for \(0<m <m_c\) there exists an energy \(e_0\) such that the problem has continuum of solutions for mass \(m\) and energy \(e_0\).