Uniform boundedness of the solutions for a one-dimensional isentropic model system of compressible viscous gas (Q1912598)

The one-dimensional equations of isentropic compressible viscous gas flows are considered. Pressure is given as a function of specific volume by \(p(v)= \text{const } v^{- \gamma}\), \(\gamma> 1\). It is shown that there is a constant \(C(\gamma)\) such that there exists a unique global solution provided some norms of initial data and force are dominated by \(C(\gamma)\). The function \(C(\gamma)\) can be chosen growing as \(\gamma- 1\) tends to zero. If the external force stabilizes as the time grows the solution also stabilizes.