Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation
- 52 Downloads
Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.
Unable to display preview. Download preview PDF.
- 1.Bause, M., Heywood, J.G., Novotny, A., Padula, M.: An iterative scheme for steady compressible viscous flow, modified to treat large potential forces. Mathematical Fluid Mechanics, Recent results and open questions. (Eds. J. Neustupa and P. Penel) Birkhäuser, Basel, 27–46, 2001Google Scholar
- 2.Bogovskii, M.E.: Solution of the first boundary value problem for an equation of continuity of an incompressible medium, Sov. Math. Dokl. 20, 1094–1098 (1979)Google Scholar
- 4.Heywood, J.G., Padula, M.: On the steady transport equation. Fundamental Directions in Mathematical Fluid Mechanics. (Eds. G.P. Galdi, J.G. Heywood and R. Rannacher) Birkhäuser, Basel, 149–170, 2000Google Scholar
- 5.Heywood, J.G., Padula, M.: On the existence and uniqueness theory for steady compressible viscous flow. Fundamental Directions in Mathematical Fluid Mechanics. (Eds. G.P. Galdi, J.G. Heywood and R. Rannacher) Birkhäuser, Basel, 171–189, 2000Google Scholar