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Session S37 - New Developments in Mathematical Fluid Dynamics

Monday, July 19, 16:30 ~ 16:55 UTC-3

Traveling wave solutions to the free boundary Navier-Stokes equations

Ian Tice

Carnegie Mellon University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Consider a layer of viscous incompressible fluid bounded below by a flat rigid boundary and above by a moving boundary. The fluid is subject to gravity, surface tension, and an external stress that is stationary when viewed in a coordinate system moving at a constant velocity parallel to the lower boundary. The latter can model, for instance, a tube blowing air on the fluid while translating across the surface. In this talk we will detail the construction of traveling wave solutions to this problem, which are themselves stationary in the same translating coordinate system. While such traveling wave solutions to the Euler equations are well-known, to the best of our knowledge this is the first construction of such solutions with viscosity.

Joint work with Giovanni Leoni (Carnegie Mellon University).

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