Compressible flow + gravitation, mass of variable sign.
Δφ + Gρ = 0 | ρ_t + div m = 0 |
m_t + div(m v) + grad p − νΔv = ρ gradφ |
e_t + div(e v) + p div v − φ div m = 0; p = γe, v = m/|ρ|.
Two galaxies of opposite-sign mass repel (dark energy); same sign attract.
Red = positive mass, blue = negative mass; white dots = fluid tracers; periodic box.