Department of Mathematics

Colloquium

  •  Thomas Sideris, University of California, Santa Barbara
  •  Affine motion of 3d incompressible ideal fluids surrounded by vacuum
  •  11/03/2016
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

We shall discuss the existence and long-time behavior of affine (spatially linear) solutions to the initial free boundary value problem for incompressible fluids surrounded by vacuum in 3d. The general problem is known to be locally well-posed. For affine motion, the equations of motion reduce to a globally solvable system of ordinary differential equations corresponding to geodesic flow in SL(3,R) viewed as a submanifold embedded in R^9 with the Euclidean metric. The domain occupied by the fluid at each time is an ellipsoid of constant volume whose diameter grows linearly in time, provided the pressure remains nonnegative. We shall examine the motion in several representative cases, including swirling flow geometry where elementary phase plane analysis can be used.

 

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Department of Mathematics
Michigan State University
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