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February  2004, 10(1&2): 459-472. doi: 10.3934/dcds.2004.10.459

Boundary layer separation and structural bifurcation for 2-D incompressible fluid flows

Tian Ma 1, and  Shouhong Wang 2,

1. 

Department of Mathematics, Sichuan University, Chengdu
2. 

Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  March 2003 Revised  August 2003 Published  October 2003

The main objective of this article and the previous articles [2, 3, 7] is to provide a rigorous characterization of the boundary layer separation of 2-D incompressible viscous fluids. First we establish a simple equation linking the separation location and time with the Reynolds number, the external forcing the boundary curvature, and the initial velocity field. Second, we show that external forcing with reverse orientation to the initial velocity field leads to structural bifurcation at a degenerate singular point with integer index of the velocity field at the critical bifurcation time. Necessary and sufficient kinematic conditions are given to identify the case for boundary layer separation.
Keywords: location and time of separation, kinematic conditions., Navier-Stokes equations, structural bifurcation, boundary layer separation.
Mathematics Subject Classification: 34D, 35Q35, 58F, 76, 86A1.
Citation: Tian Ma, Shouhong Wang. Boundary layer separation and structural bifurcation for 2-D incompressible fluid flows. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 459-472. doi: 10.3934/dcds.2004.10.459
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