Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids (Q848794)

The authors consider initial-boundary value problems for nonhomogeneous incompressible Navier-Stokes equations in a regular bounded domain in 2 or 3 space dimensions. The strong solution is assumed to be conditionally asymptotically stable in a sense defined in the paper, depending on the regularity of allowed perturbations of the density equation. For spectral semi-Galerkin approximations, the authors derive optimal uniform in time error bounds for velocity in Dirichlet norm, and for variable density in some spaces \(L^r\).