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Karl Glasner : Dissipative fluid systems and gradient flows

This talk describes the the gradient flow nature of dissipative fluid interface problems. Intuitively, the gradient of a functional is given by the direction of ``steepest descent''. This notion, however, depends on the geometry assigned to the underlying function space. The task is therefore to find a metric appropriate for the given dynamics.

For the problem of surface tension driven Hele-shaw flow, the correct metric turns out to have a remarkable connection to an optimal transport problem. This connection points the way to a diffuse interface description of Hele-Shaw flow, given by a degenerate Cahn-Hilliard equation. Some computational examples of this model will be given. The problem of viscous sintering, the Stokes flow counterpart to the Hele-Shaw problem, will also be discussed.

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