On the exponential stability of the rest state of a viscous compressible fluid
The author considers viscous isothermal gas in a bounded three-dimensional domain, assuming that the gas is subjected only to a potential force. The main results show that the energy of weak regular perturbations to the basic rest state decays exponentially in time, regardless of the magnitude of the potential force. The decay rate depends only on the viscosity coefficient, on a thermodynamic parameter, and on the domain. The results can be extended to the case of discontinuous density (e.g. to supersonic flows). In the inviscid limit, the author recovers the marginal stability.
scientific article; zbMATH DE number 1310875