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Convergence rate toward planar stationary waves for compressible viscous fluid in multidimensional half space. (English) Zbl 1202.35031

The present paper concerns the long-time behavior of a flow of isentropic and compressible viscous fluid in a two- or three-dimensional half space. One obtains a convergence rate of a solution toward a planar stationary wave for an outflow problem, where the fluid flows out through a boundary. For a supersonic flow at spatial infinity, one obtains an algebraic or an exponential decay rate provided that an initial perturbation decays, in normal direction, with the algebraic or the exponential rate, respectively. The algebraic convergence rate is also obtained for a transonic flow when the convergence rate is worse than that for the supersonic flow. The proofs are based on deriving a priori estimates of the perturbation from the stationary wave by using a time and space weighted energy method.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
35Q30 Navier-Stokes equations
76N15 Gas dynamics (general theory)
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