BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gianni Arioli (Politecnico di Milano\, Italy) DTSTART:20201124T150000Z DTEND:20201124T160000Z DTSTAMP:20260423T024737Z UID:CRM-CAMP/23 DESCRIPTION:Title: Symmetry breaking and Hopf bifurcations for the planar Navier-Stokes equ ation\nby Gianni Arioli (Politecnico di Milano\, Italy) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\nA bstract\nWe consider the Navier-Stokes equation for an incompressible visc ous fluid on a square\, satisfying Navier boundary conditions and being su bjected to a time-independent force. The uniqueness of stationary solution s is studied in dependence of the kinematic viscosity. For some particular forcing\, it is shown that uniqueness persists on some continuous branch of stationary solutions\, when the viscosity becomes arbitrarily small. On the other hand\, for a different forcing\, a branch of symmetric solution s is shown to bifurcate\, giving rise to a secondary branch of nonsymmetri c stationary solutions. Furthermore\, as the kinematic viscosity is varied \, the branch of symmetric stationary solutions is shown to undergo a Hopf bifurcation\, where a periodic cycle branches from the stationary solutio n. Our proof is constructive and uses computer-assisted estimates.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/23/ END:VEVENT END:VCALENDAR