Abstract: The vanishing viscosity problem consists of understanding the limit, or limits, of solutions of the Navier–Stokes equations, with viscosity $\nu$, as $\nu$ tends to zero. The Navier–Stokes equations are a model for real-world fluids and the parameter $\nu$ represents the ratio of friction, or resistance to shear, and inertia. Ultimately, the relevant question is whether a real-world fluid with very small viscosity can be approximated by an ideal fluid, which has no viscosity. In this talk we will be primarily concerned with the classical open problem of the vanishing viscosity limit of fluid flows in domains with boundary. We will explore the difficulty of this problem and present some known results. We conclude with a discussion of criteria for the vanishing viscosity limit to be a solution of the ideal fluid equations.

Bio: 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.