Low-regularity Local Well-posedness of the Elastic Wave System

This lecture from the Harvard CMSA General Relativity Seminar features Sifan Yu from the National University of Singapore discussing low-regularity local well-posedness of the elastic wave system in three spatial dimensions. Explore how admissible harmonic elastic materials allow for splitting dynamics into "divergence-part" and "curl-part," each satisfying distinct coupled quasilinear wave systems with different acoustical metrics. Learn about the main research finding that demonstrates how the Sobolev norm H^{3+} of the "divergence-part" (faster-wave part) and the H^{4+} of the "curl-part" (slower-wave part) can be controlled in terms of initial data for short time periods. The presentation highlights that the H^{3+} Sobolev norm assumption is optimal for the "divergence-part" and represents joint work with Xinliang An and Haoyang Chen.