Analysis Seminar

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Almost Global Existence of Small Solutions for 2D Incompressible Hookean Elastodynamics

Speaker: Thomas Sideris, UC Santa Barbara

Location: Warren Weaver Hall 1302

Date: Thursday, March 28, 2013, 11 a.m.

Synopsis:

We will examine the IVP for equations of 2d incompressible isotropic elastodynamics.

We show that classical solutions exist “almost globally” in time, for small initial perturbations of the identity.

We use the energy method with a ghost weight. This is combined with decay estimates, obtained via generalized Sobolev inequalities and weighted \(L^2\) bounds. The argument exploits the inherent null structure of the nonlinearities.

This is joint work with Zhen Lei and Yi Zhou of Fudan University.