The authors prove a global-in-time existence result for a weak solution to a model they proposed in [Math. Models Methods Appl. Sci. 29, No. 12, 2321–2357 (2019; Zbl 1425.35151)] and which accounts for the motion of dilute superparamagnetic nanoparticles in fluids influenced by quasi-stationary magnetic fields. They consider two domains \(\Omega \Subset \Omega ^{\prime }\Subset \mathbb{R}^{d}\), \(d=2,3\), and the system \(\rho _{0}u_{t}+\rho _{0}(u\cdot \nabla )u+\nabla p-\mathrm{div}(2\eta Du)=\mu _{0}(m\cdot \nabla )(\alpha _{1}h+\frac{\beta }{2}h_{a})+\frac{\mu _{0}}{2} \mathrm{curl}(m\times (\alpha _{1}h+\frac{\beta }{2}h_{a})\), \(\mathrm{div}(u)=0\), \( c_{t}+u\cdot \nabla c+\mathrm{div}(cV_{\mathrm{part}})=0\), \(-\Delta R=\mathrm{div}(m)\), \( m_{t}+\mathrm{div}(m\otimes (u+V_{\mathrm{part}}))-\sigma \Delta m=\frac{1}{2}\mathrm{curl}\,u\times m- \frac{1}{\tau _{\mathrm{rel}}}(m-\chi (c,h)h)\), in \(\Omega \times (0,T)\), and \( -\Delta R=0\) in \((\Omega ^{\prime }\backslash \Omega )\times (0,T)\), with \( V_{\mathrm{part}}=-KD\frac{f_{2}(c)}{c}\nabla g(c)+K\mu _{0}\frac{f_{2}(c)}{c^{2}} (\nabla (\alpha _{1}h+\frac{\beta }{2}h_{a}-\alpha _{3}m))^{T}m\). The boundary and transmission conditions \(u=0\), \(cV_{\mathrm{part}}\cdot \nu =0\), \( (V_{\mathrm{part}}\cdot \nu )(m-(m\cdot \nu )\nu )-\sigma \mathrm{curl}\,m\times \nu =0\), \( (V_{\mathrm{part}}\cdot \nu )(m\cdot \nu )-\sigma \mathrm{div}m=0\), \([\nabla R+m]\cdot \nu =0\), on \(\partial \Omega \times \lbrack 0,T]\), \(\nabla R\cdot \nu =h_{\alpha }\cdot \nu \) on \(\partial \Omega ^{\prime }\times \lbrack 0,T]\), are added and the initial conditions \(u(\).\(,0)=u^{0}\), \(c(\).\(,0)=c^{0}\), \(m(\).\( ,0)=m^{0}\) are considered. Here \((u,p)\) denotes the hydrodynamic variables of the carrier fluid, \(c\) stands for the number density of the magnetic nanoparticles and \(m\) or \(h=\nabla R\) describe the magnetization or magnetic field, respectively. The vector field \(V_{\mathrm{part}}\) denotes the particle velocity relative to the flow of the carrier fluid. It takes diffusive and magnetic effects into account. The system is driven by the external magnetic field \(h_{a}\) which satisfies Maxwell’s equations in the absence of matter, \( \mathrm{curl}\,h_{a}=0\), \(\mathrm{div}(h_{a})=0\). The proof of the existence result requires smoothness hypotheses on the simply connected domains and on the data. It is based on the construction of discrete spaces for the magnetization and the magnetic potential, then for the velocity field and the particle density. Using the Picard-Lindelöf theorem, the authors prove the existence of global solutions to a discretization of an appropriate transport and mobility regularized version of the above problem. They indeed introduce some cut-off from 0 and regularized parameters. They establish uniform estimates on different terms involving this solution. They prove compactness result on this solution to pass to the limit and to prove the existence of a global-in-time and weak solution to the above problem. They prove an energy estimate on this weak solution. In the last part of their paper, the authors consider the degenerate case. They here prove an existence result using a different approach to regularize the particle density.