Characteristic Initial Value Problem for the 3D Compressible Euler Equations

Watch a General Relativity Seminar presentation from NUS researcher Sifan Yu exploring groundbreaking research on the characteristic initial value problem for three-dimensional compressible Euler equations. Delve into the first-ever analysis conducted without symmetry assumptions, examining both vorticity presence and various equations of state. Learn about the novel approach of distinguishing between "free-component" and "constrained-component" initial data, contrasting with traditional Cauchy problem methodologies. Understand the development of a priori estimates, local well-posedness proofs, continuation criterion arguments, and Sobolev norm regularity theory, all achieved through critical application of the vectorfield method. Gain insights from this collaborative research with Jared Speck that advances our understanding of complex fluid dynamics and mathematical physics.