[GS_M_APP]Eventual regularity and asymptotic behavior of Leray-Hopf weak solutions for the Hall MHD equations
ABSTRACT
In this talk, we study Leray-Hopf weak solutions for the incompressible, viscous and resistive Hall magnetohydrodynamic (Hall MHD) equations based on a joint work with Jinwook Jung (Hanyang University). We begin with a brief review of the fundamental properties of Leray-Hopf weak solutions for the incompressible Navier-Stokes equations. We then consider the Hall MHD equations depending only on two spatial variables and show that any Leray-Hopf weak solution can become eventually smooth. Based on this eventual smoothness, we derive the asymptotic behavior of Leray-Hopf weak solutions. For the three dimensional case, we construct weak solutions which eventually obtain additional regularities by investigating the magneto-vorticity field structure.
