Title: Singularity formation in incompressible fluids.  Abstract:  I will discuss a recent example of singularity formation in the 3d Euler equation. This is based on work joint with Federico Pasqualotto.Â
Title: The stability of irrotational shocks and the Landau law of decay.  Abstract:  We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our analysis is motivated by Landau's analysis of spherically-symmetric shock waves, who predicted that at large times, […]
Title:Â From Instability to Singularity Formation in Incompressible FluidsAbstract:Â In this talk, I will first review the singularity formation problem in incompressible fluid dynamics, describing how particle transport poses the main challenge in constructing blow-up solutions for the 3d incompressible Euler equations. I will then outline a new mechanism that allows us to overcome the effects of […]