About compressible viscous fluid flow in a bounded region
Using the theory of analytic \(L_ p\)-semigroups the paper gives a criterion for the existence for all times and convergence as \(t\to \infty\) of solutions close to a constant state for a class of parabolic- hyperbolic systems with one hyperbolic equation. The most important condition is that the linearization of the equation about the constant state may not have any solution that does not go to zero as \(t\to \infty\). By means of previous work of the author it is shown that this condition is fulfilled for compressible viscous fluids and for a magnetic-hydrodynamic model. Due to the fact that p can be chosen very large the results are independent of the dimension of the space in question.
scientific article; zbMATH DE number 4097000