Global Regularity for a Model of Inhomogeneous Three-dimensional Navier-Stokes Equations

A model of inhomogeneous three-dimensional Navier-Stokes equations was studied in this paper. By using the energy method, Littlewood-Paley paraproduct decomposition techniques and Sobolev embedding theorem study of the global regularity of solutions were adopted. The dissipative term Δ u in the classical inhomogeneous Navier-Stokes equations is replaced by - D ² u and a new Navier-Stokes equations model was obtained, where D was a Fourier multiplier whose symbol is m( ξ) =|ξ| ^{5 / 4}. Blow-up criterion and global regularity of this model were proved for the initial data ( ρ ₀, u ₀)∈ H ^{3 / 2 +ε}×H ^δ , where ε and δ are arbitrary small positive constants.