Evolving Transport induced by a Surface Wave Propagating along a   Vacuum-Matter Interface
  Hydrodynamic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum-matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the critical bounds for matter-freezed or zero-volume-flow-rate states corresponding to specific Reynolds numbers and wave numbers which might be linked to the evolution of the Universe. Our results also show that for positive evolution of the matter their might be existence of negative pressure. 
A. Kwang-Hua Chu