The HADES seminar on Tuesday, March 18th, will be at 3:30pm in Room 740.

Speaker: Sung-Jin Oh

Abstract: The electron magnetohydrodynamics equation (E-MHD) is a fluid description of plasma in small scales where the motion of electrons relative to ions is significant. Mathematically, (E-MHD) is a quasilinear dispersive equation with nondegenerate but nonelliptic second-order principal term. In this talk, I’ll discuss a recent proof, joint with In-Jee Jeong, of the local wellposedness of the Cauchy problems for (E-MHD) without resistivity for possibly large perturbations of nonzero uniform magnetic fields. While the local wellposedness problem for (E-MHD) has been extensively studied in the presence of resistivity (which provides dissipative effects), this seems to be the first such result without resistivity.

More specifically, my goal is to explain the main new ideas introduced in this work and the related work of Pineau-Taylor on quasilinear ultrahyperbolic Schrodinger equations, which also have nondegenerate but nonelliptic principal terms. Both works significantly improve upon the classical work of Kenig-Ponce-Rolvung-Vega on such PDEs, in the sense that the regularity and decay assumptions on the initial data are greatly weakened to the level analogous to the recent work of Marzuola-Metcalfe-Tataru in the case of an elliptic principal term.