Vanishing viscosity for non-homogeneous asymmetric fluids in R3: The L² case

We study the vanishing viscosity problem for the local-in-time solutions to the equations of non-homogeneous, viscous, incompressible asymmetric fluid in R3 in the L² context. We prove that the fluid variables converge uniformly as the viscosities go to zero to a solution of a non-homogeneous, non-viscous, incompressible asymmetric fluid governed by an Euler-like system. This completes the previous work [5] where results for L^p, p>3, where obtained.