  The anti-de-Sitter/conformal field theory (AdS/CFT) correspondence is used to
provide an estimate of the radius of convergence of the linearized gradient
expansion of the hydrodynamic description of $\mathcal{N}=4$ supersymmetric
Yang-Mills (SYM) theory minimally coupled to $U(1)$ gauge theory subjected to
strong magnetic fields. The results of this work demonstrate that the
dispersion relations of hydrodynamic modes continue to converge for magnetic
field strengths far beyond those values for which a hydrodynamic description is
expected. For magnetic field strengths much larger then the temperature scale
the bulk dual interpolates between AdS$_{4+1}$ and the product of a
Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole and a two dimensional manifold
(BTZ$_{2+1}\times \mathbb{R}^2$), and may be regarded as a renormalization
group flow of the $3+1$ dimensional CFT to a $1+1$ dimensional CFT. In this
regime, we clarify past literature on the quasi-normal mode (QNM) spectrum of
bulk scalar fields by introducing a new way to classify the behavior of QNM
collisions in the complex frequency and momentum plane.
