Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids

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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 $L^r$.
22 pages; Some typos were corrected

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Analysis of PDEs, 35Q35; 65M15; 65M60;76D99

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http://salesiana.dossiersoluciones.com/handle/123456789/102188

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0508442
 http://arxiv.org/abs/math/0508442

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arXiv