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Center for Scientific Computation and Mathematical Modeling

Research Activities > Programs > Incompressible Flows 2006> Thomas Sideris

Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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Global Existence in Nonlinear Elastodynamics

Thomas Sideris

Department of Mathematics, University of California, Santa Barbara

Abstract: We present some results on the global existence of solutions to the initial value problem in 3d nonlinear elastodynamics. Compressible and incompressible motions, as well as their relationship, will be discussed. The results are valid for isotropic materials with sufficiently small displacements from equilibrium in the absence of boundaries. In the compressible case, an additional null condition must also be imposed.