Fluids, elasticity, geometry, and wild solutions

  • Marshall Slemrod (University of Wisconsin-Madison)
A3 01 (Sophus-Lie room)


This talk gives a short review of recent work of A. Acharya (CMU), G.-Q. Chen (Oxford), M. Slemrod (Univ. of Wisconsin-Madison), D. Wang (Pittsburgh) on the direct connection between the 2d Euler equations of incompressible fluid flow and motion of a 2d surface in 3-dimensional Euclidean space. In particular we note how this link provides a direct application of the Nash-Kuiper non-smooth isometric embedding result which in turn provides information on ill-posedness for the initial value problem for weak solutions of the Euler equations as well as neo-Hookian elasticity. Furthermore it suggests that the Nash-Kuiper solutions may represent fluid turbulence. The work was strongly motivated by the sequence of papers of C. De Lellis and L. Szekelyhidi, Jr.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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