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A hydrodynamic description for inelastic Maxwell mixtures driven by astochastic bath with friction is derived. Contrary to previous works whereconstitutive relations for the fluxes were restricted to states near thehomogeneous steady state, here the set of Boltzmann kinetic equations is solvedby means of the Chapman--Enskog method by considering a more generaltime-dependent reference state. Due to this choice, the transport coefficientsare given in terms of the solutions of a set of nonlinear differentialequations which must be in general numerically solved. The solution to theseequations gives the transport coefficients in terms of the parameters of themixture (masses, diameters, concentration, and coefficients of restitution) andthe time-dependent (scaled) parameter $\xi^*$ which determines the influence ofthe thermostat on the system. The Navier--Stokes transport coefficients areexactly obtained in the special cases of undriven mixtures ($\xi^*=0$) anddriven mixtures under steady conditions ($\xi^*=\xi_\text{st}^*$, where$\xi_\text{st}^*$ is the value of the reduced noise strength at the steadystate). As a complement, the results for inelastic Maxwell models (IMM) in bothundriven and driven steady states are compared against approximate results forinelastic hard spheres (IHS) [Khalil and Garz\'o, Phys. Rev. E \textbf{88},052201 (2013)]. While the IMM predictions for the diffusion transportcoefficients show an excellent agreement with those derived for IHS,significant quantitative differences are specially found in the case of theheat flux transport coefficients.

Unified hydrodynamic description for driven and undriven inelastic Maxwell mixtures at low density