Organizers: Steve Shkoller, John Hunter, and Joseph Biello.
The theme of this RFG is water waves and moving interfaces in perfect fluids. Mathematically, this means the Euler equations in either incompressible or compressible form. Euler derived these equations over 250 years ago, and we are just now starting to mathematically understand these equations when set on moving domains. This RFG will cover the analysis and asymptotics of these amazing equations. Of course, from the Euler equations, many of the other famous equations of mathematical physics can be found. The KdV and NLS equations are just two examples that arise from asymptotic limits of the wave motion (here the wave is the material interface between air and water). This RFG has no formal prerequisites. On the other hand, this topic requires a blend of analysis, PDE, geometry, asymptotics, and a bit of common sense.
Main courses:
Related courses:
The Rayleigh-Taylor instability in the Crab Nebula.
Named after Lord Rayleigh and G. I. Taylor, this occurs any time a dense, heavy
fluid is being accelerated by light fluid. This is the case with a cloud and
shock system, or when a fluid of a certain density floats above a fluid of
lesser density, such as dense oil floating above water.
This is modeled by
the two-phase Euler equations with moving material interface. (Image
from
Wikipedia.)