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

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss