Marcelo M. Santos

Steady flow for incompressible fluids in domains with unbounded curved channels

We give an overview on the solution of the stationary Navier-Stokes equations for non newtonian incompressible fluids established by G. Dias and M.M. Santos (Steady flow for shear thickening fluids with arbitrary fluxes, J. Differential Equations 252 (2012), no. 6, 3873-3898), propose a definition for domains with unbounded curved channels which encompasses domains with an unbounded boundary, domains with nozzles, and domains with a boundary being a punctured surface, and argue on the existence of steady flowfor incompressible fluids with arbitrary fluxes in such domains.

2d Ladyzhenskaya-Solonnikov Problem for Inhomogeneous Fluids

We consider the Ladyzhenskaya-Solonnikov problem [5] for a stationary inhomogeneous incompressible fluid in a 2d domain. Given arbitrary fluxes for the velocity and momentum fields, we prove the existence of a weak solution.