Lev Kapitanski (Miami)
Lagrange, Euler, Hooke, and Cauchy
Abstract:
In nonlinear elasticity theory there is a class of models that can be derived
from an action functional with the potential energy described by a strain
energy density function. These are the hyperelastic materials. The simplest
example is the Neo-Hookean material (like some plastics, biological tissues,
or rubber). In this talk, after describing the equations of motion of an incompressible
neo-Hookean material, I will concentrate on the Cauchy problem for those equations.
There are similarities with the Euler equations of fluid dynamics,
and there are major differences. I will show some new analytical tools that help
with the low regularity well-posedness results.
Based on joint work with Lars Andersson.