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Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space
In this paper, we study the axisymmetric Hall magnetohydrodynamics where $u = u^re_r+u^ze_z$ and $B = B^θe_θ$. We construct small, smooth, compactly supported, and axisymmetric initial data $(u_{0},B_{0})$ and prove that there is a unique smooth axisymmetric solution with norm inflation in $H^{σ-1}(
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