On the Lifespan of Axisymmetric Hall-MHD with Swirl

Abstract

In this paper, we study the three-dimensional inviscid incompressible resistive Hall-MHD system in the axisymmetric setting with nontrivial swirl velocity and purely azimuthal magnetic. Assuming only that the swirl component of the initial velocity is sufficiently small, we prove that the lifespan of the strong solution can be sufficiently large. An explicit lifespan lower bound in terms of the size of the initial swirl is given. Moreover, we also study the behavior of the lifespan as the resistivity tends to zero.