Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Ω⊊R³, when the initial vacuum is allowed, i.e., the initial density ρ₀ is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms.