I will present a recently obtained result on spatial decay for the incompressible Navier-Stokes equations in R^n. It is well-known that generic mild solutions cannot decay faster than |x|^(-n-1). This is a consequence of the inner structure of the equations, through the decay properties of the so-called Oseen kernel. Here, we propose an approach to go beyond this rate of decay. The idea is to introduce an external forcing in the system. This will allow to eliminate the slowly decaying term in an asymptotic profile previously obtained by Brandolese and Vigneron. We will begin by a theorem of existence of mild solutions in some well-suited function spaces, and then obtain a rapidly decaying solution to a Navier-Stokes system with a specific force. The proof is based on an algorithmic construction of external forces, inspired by a recent work of Brandolese and Okabe.

Venue: DIM seminar room, Beauchef 851, 5th floor.