Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation
Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and […]