Error Estimates for Spectral Semi-Galerkin Approximations of Incompressible Asymmetric Fluids with Variable Density

Abstract

We consider spectral semi-Galerkin approximations for global strong solutions of the equations for variable density asymmetric incompressible fluids in a bounded domain $$\Omega $$ of $$\mathbb {R}^3$$ . We prove an optimal uniform in time error estimate in the $${\varvec{H}}^{1}$$ norm for approximations of both the linear and angular velocity of particles of the fluid. We also derive an error bound for approximations of the density in some Lebesgue spaces $$L^{r}(\Omega )$$ .