Abstract : The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply–connected and the fluxes are not assumed to be small. In this very general setting, we prove the existence of a solution with a uniformly bounded Dirichlet integral in every compact subset. This is a generalization of the classical Ladyzhenskaya–Solonnikov result obtained under the additional assumption of zero boundary conditions. For small data of the problem we also prove the unique solvability and attainability of Couette-Poiseuille flows at infinity. The main novelty of our approach
is the proof of the corresponding Leray-Hopf inequality by Leray’s_reductio ad absurdum_ argument. For this contradiction approach, we use some fine properties of weak solutions to the Euler system based on Morse–Sard-type theorems in Sobolev spaces obtained by Bourgain, Korobkov & Kristensen.

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

Zoom: https://uchile.zoom.us/j/93324747064?pwd=bzbZ2ADIpsi2ye6t00fJnwWOLJ4JLy.1