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Talk

Fluids, elasticity, geometry, and wild solutions

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

Abstract

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.

Upcoming Events of this Seminar

  • Dienstag, 11.03.25 tba with Jianfeng Lu
  • Dienstag, 11.03.25 tba with Steffen Börm
  • Dienstag, 06.05.25 tba with Ilya Chevyrev
  • Dienstag, 03.06.25 tba with Mate Gerencser