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Observation of the solar wind–magnetosphere boundary provides a unique opportunity to investigate the physics underlying the interaction between two collisionless magnetized plasmas with different temperature, density and magnetic field topology. Their mixing across the interface as well as the boundary dynamics are affected by the development of fluid (and kinetic) instabilities driven by large-scale inhomogeneities in particle and electromagnetic fields. Building up a realistic initial equilibrium state of the magnetopause according to observations is still a challenge nowadays. In this paper, we address the modeling of the particles and electromagnetic field configuration across the Earth's magnetopause by means of a three-fluid analytic model. The model relies on one hot and one cold ion population as well as a neutralizing electron population. The goal is to create an analytic model that is able to reproduce the observations as closely as possible. Some parameters of the model are set using a fitting procedure that aims to minimize their difference with respect to experimental data provided by the Magnetospheric MultiScale (MMS) mission. All of the other profiles, concerning the electron pressure and the relative densities of the cold and hot ion populations, are calculated in order to satisfy the fluid equilibrium equations. Finally, using a new tri-fluid code, we check the stability of the large-scale equilibrium model for a given experimental case and provide proof that the system is unstable to reconnection. This model could be of interest for the interpretation of satellite results and for the study of the dynamics at the magnetosphere–solar wind boundary. [ABSTRACT FROM AUTHOR]