Non-radial implosion for compressible Euler and Navier-Stokes in T3 and R3

Jia Shi, MIT
Fine Hall 314

We will discuss the smooth, non-radial solutions of the compressible Euler and Navier-Stokes equation that develop an imploding finite time singularity. The construction is motivated by the radial imploding solutions from Merle-Raphaël--Rodnianski--Szeftel, and Cao-Labora--Buckmaster--Gomez-Serrano but is flexible enough to handle both periodic and non-radial initial data. This is a joint work with Gonzalo Cao-Labora, Javier Gomez-Serrano, and Gigliola Staffilani.