Strong solutions to a fluid-particle interaction model with magnetic field in $ \mathbb{R}^2 $

A fluid-particle interaction model with magnetic field is studied in this paper. When the initial vacuum and the far field vacuum of the fluid and the particles are contained, the constant shear viscosity \begin{document}$ \mu $\end{document} and the bulk viscosity \begin{document}$ \lambda $\end{document} are \begin{document}$ \mu>0 $\end{document}\begin{document}$ \lambda = \rho^\beta $\end{document} for any \begin{document}$ \beta\geq 0 $\end{document} , the strong solutions of the 2D Cauchy problem for the coupled system are established applying the method of weighted estimates in Li-Liang's paper on Navier-Stokes equations.