Abstract
In this paper, we will give the first result concerning the non-uniform dependence on initial data for the 2D magnetohydrodynamics (MHD)-Boussinesq equations as a hyperbolic-parabolic system. More precisely, we prove that the data-to-solution map of the Cauchy problem to the 2D MHD-Boussinesq equations is not uniformly continuous in Hs with s > 2.
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