A Connection Between Symmetry Breaking for Sobolev Minimizers and Stationary Navier–Stokes Flows Past a Circular Obstacle

Fluid flows around a symmetric obstacle generate vortices which may lead to symmetry breaking of the streamlines. We study this phenomenon for planar viscous governed by stationary Navier–Stokes equations with constant inhomogeneous Dirichlet boundary data in rectangular channel containing circular obstacle. In such (symmetric) framework, is strictly related appearance multiple solutions. Symmetry properties some Sobolev minimizers are studied and explicit bounds on velocity (in terms length height channel) ensuring uniqueness obtained after estimating embedding constants constructing suitable solenoidal extension data. show that, regardless employed, converge zero at an optimal rate as tends infinity.