BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Computer-Assisted Proofs of 3D Euler Singularity and Nonuniqueness of Leray–Hopf Solutions for the Unforced 3D Navier–Stokes Equations - Tom Hou\, Caltech DTSTART:20260410T150000Z DTEND:20260410T160000Z UID:TALK245998@talks.cam.ac.uk CONTACT:Duncan Hewitt DESCRIPTION:Whether the 3D incompressible Euler equations can develop a fi nite-time singularity from smooth initial data remains one of the central open problems in nonlinear PDEs. In this talk\, I will present recent join t work with Dr. Jiajie Chen\, in which we rigorously prove finite-time blo wup for the 2D Boussinesq equations and the 3D axisymmetric Euler equation s with smooth initial data and smooth boundary. Our approach uses a dynami cally rescaled formulation that reduces singularity formation to the long- time stability of an approximate self-similar blowup profile. A key diffic ulty is proving the linear stability of a numerically constructed profile. To address this\, we decompose the solution operator into a leading-order part\, which admits sharp stability estimates\, and a finite-rank perturb ation\, which is controlled by a computer-assisted proof. I will also disc uss recent joint work with Yixuan Wang and Changhe Yang on nonuniqueness o f Leray–Hopf solutions to the unforced 3D incompressible Navier–Stokes equations. In this setting\, the viscous term introduces several new ingr edients but also greatly simplify the analysis: standard (H^1) estimates s uffice\, without the singular weights needed in the inviscid case. A centr al step is to establish the existence of a self-similar Leray–Hopf solut ion and then prove the existence of a second solution by analyzing the sta bility of the linearized operator around this profile and showing that it admits an unstable mode. These results highlight the fruitful interplay am ong analysis\, computation\, and rigorous validation in nonlinear PDEs. LOCATION:MR2 END:VEVENT END:VCALENDAR