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Abstract A two-dimensional class of mean-field models serving as a minimal frame to study long-range interaction in two space dimensions is considered. In the case of an anisotropic mixed attractive-repulsive interaction, an initially spatially homogeneous cold fluid is dynamically unstable and evolves towards a quasi-stationary state in which the less energetic particles get trapped into clusters forming a Bravais-like lattice, mimicking a crystalline state. Superimposed to this, one observes in symplectic numerical simulations a flux of slightly more energetic particles channeling through this crystalline background. The resultant system combines the rigidity features of a solid, as particles from a displaced core are shown to snap back into place after a transient, and the dynamical diffusive features of a liquid for the fraction of channeling and free particles. The combination of solid and liquid properties is numerically observed here within the classical context. The quantum transposition of the model may be experimentally reached using the latest ultracold atoms techniques to generate long-range interactions.