Mathematics Colloquium: â€œRegularity issue of the critical and supercritical fluid mechanics PDEsâ€
4:10 pm, Neill Hall 5W
Dr. Kazou Yamazaki
Fluid mechanics plays a pivotal role in engineering applications and has been studied intensively from physics point of view. From mathematics point of view, the initial value problem of PDEs in fluid mechanics, typically nonlinear, remains one of the most interesting and challenging topics in Analysis, for example the Navier-Stokes Existence and Smoothness Problem. In this talk, we discuss its difficulty, specifically elaborate on the criticality of such PDEs. Thereafter we discuss recent developments on the regularity issue concerning a particular system of PDEs, the magnetohydrodynamics system.