Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids

Details Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids

2005-08-24

arxiv.org/abs/math/0508442v2

Mathematics

Analysis of PDEs

22 pages; Some typos were corrected

Scientific paper

We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the $H^1$ norm for the velocity. We also derive an error estimate for the density in some spaces $L^r$.

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