Vortex-like finite-energy asymptotic profiles for isentropic compressible flows

Luis Miguel Miguel Rodrigues (1)

1 IF - Institut Fourier

Bidimensional incompressible viscous flows with well-localised vorticity are well-known to develop vortex structures. The purpose of the present paper is to recover the asymptotic profiles describing these phenomena for homogeneous finite-energy flows as asymptotic profiles for near-equilibrium isentropic compressible flows. This task is performed by extending the sharp description of the asymptotic behaviour of near-equilibrium compressible flows obtained by David Hoff and Kevin Zumbrun to the case of finite-energy vortex-like solutions.

Mots clés: artificial viscosity approximation; Isentropic compressible Navier-Stokes equations; near-equilibrium; long-time asymptotic profiles; vortex; hyperbolic-parabolic composite-type; artificial viscosity approximation.

Domaines: Equations aux dérivées partielles [math.AP]

Luis Miguel Miguel Rodrigues. Vortex-like finite-energy asymptotic profiles for isentropic compressible flows. 2008. ⟨hal-00271858⟩