On Bifurcating Time-Periodic Flow of a Navier-Stokes Liquid past a Cylinder

摘要: We provide general sufficient conditions for branching out of a time-periodic family solutions from steady-state to the two-dimensional Navier-Stokes equations in exterior cylinder. To this end, we first show that problem can be formulated as coupled elliptic-parabolic nonlinear system appropriate function spaces. This is obtained by separating time-independent averaged component velocity field its "purely periodic" one. then prove bifurcation occurs, provided linearized operator parabolic possess simple eigenvalue crosses imaginary axis when Reynolds number passes through (suitably defined) critical value. also only supercritical or subcritical may occur. Our approach different and, believe, more direct than those used previous authors similar, but distinct, context.