Abstract: In these lectures we will present the analysis on the asymptotic behavior of incompressible and inviscid fluid flow around a vanishingly small disk in the two-dimensional case. We begin by recollecting some known results on the incompressible Euler equations, which model such flows, and we discuss a few technical results we will use. We then describe the flow around a small disk from a vortex dynamics point of view and we proceed with the statement and proof of a theorem on the limiting behavior as the radius of the disk vanishes.

Helena Nussenzveig Lopes is a full professor at the Federal University of Rio de Janeiro (UFRJ). Prior to working at UFRJ she spent 20 years at the State University of Campinas (UNICAMP). In 2010 she was admitted to the National Order of Scientific Merit in Brazil and, in 2016, she was elected Fellow of SIAM. She was an Invited Speaker in the PDE Section at ICM2018. Helena obtained her PhD at the University of California, Berkeley, under the supervision of Ron DiPerna, followed by L. Craig Evans. She works on weak solutions for fluid dynamics equations, on problems with low-regularity flows and transition to turbulence. Most of her papers concern the 2D incompressible Euler and Navier-Stokes equations.