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Consider a layer of viscous incompressible fluid bounded belowÌýby a flat rigid boundary and above by a moving boundary.Ìý The fluid isÌýsubject to gravity, surface tension, and an external stress that isÌýstationary when viewed in a coordinate system moving at a constantÌývelocity parallel to the lower boundary.Ìý The latter can model, forÌýinstance, a tube blowing air on the fluid while translating across theÌýsurface.Ìý In this talk we will detail the construction of traveling waveÌýsolutions to this problem, which are themselves stationary in the sameÌýtranslating coordinate system.Ìý While such traveling wave solutions toÌýthe Euler equations are well-known, to the best of our knowledge this isÌýthe first construction of such solutions with viscosity.ÌýÌý

This is jointÌýwork with Giovanni Leoni.