| Abstract: |
| The steady motion of a viscous incompressible fluid in a junction of unbounded channels 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 prove the unique solvability and attainability of Couette-Poiseuille flows at infinity. Further, by extending and refining an approach initially introduced by J.B. McLeod, we prove the rigidity of a generic class of Couette-Poiseuille flows, without any restriction on the size of the flux or the periodicity of perturbation. Based on joint works with Giovanni P. Galdi, Filippo Gazzola, Mikhail Korobkov and Gianmarco Sperone. |
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