# Well-posedness problems for the magneto-hydrodynamics models

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Mimi Dai, University of Illinois at Chicago
Fine Hall 322

We will talk about some recent results on the well-posedness problems in Sobolev spaces for the magneto-hydrodynamics with and without Hall effect, i.e., the Hall MHD and classical MHD models. One of the purposes of the work is to search the optimal Sobolev space of well-posedness for the two models. Another purpose is to understand the nonlinear Hall term $\nabla\times((\nabla\times b)\times b)$ in the Hall MHD, which appears more singular than $u\cdot\nabla u$ in the NSE, but with special geometry.