The problem of minimizing energy dissipation and wall drag in turbulent pipe and channel flows is a classical one that is of great importance in practical engineering applications.
Remarkably, the addition of trace amounts of polymer into a turbulent flow has a pronounced effect on reducing friction drag. To study this mathematically, we introduce a new boundary condition for Navier-Stokes equations which models the situation where polymers are irreversibly grafted to the wall. This boundary condition is time-dependent and generalizes the classical Navier-Friction condition. Global well-posedness is established in 2D and the boundary conditions are shown to lead to the strong inviscid limit and exhibit drag reduction.
Talk is based on joint work with Joonhyun La.