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CONVERGENCE AND ERROR ESTIMATES OF TWO ITERATIVE METHODS FOR THE STRONG SOLUTION OF THE INCOMPRESSIBLE KORTEWEG MODEL

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apartado de Correos 1160, 41080 Sevilla, Spain

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M. A. RODRÍGUEZ-BELLIDO

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apartado de Correos 1160, 41080 Sevilla, Spain

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https://doi.org/10.1142/S0218202509003929Cited by:0 (Source: Crossref)

Abstract

We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative linear schemes. The different unknowns are sequentially decoupled in the first scheme and in parallel form in the second one. In both cases, the whole sequences are bounded in strong norms and convergent towards the strong solution of the system, by using a generalization of Banach's fixed point theorem. Moreover, we explicit a priori and a posteriori error estimates (respect to the weak norms), which let us to compare both schemes.

Keywords:

AMSC: 35B45, 35B65, 35Q35, 65M12, 65M15, 76D03

References

D. M. Anderson, G. B. McFadden and A. A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998), DOI: 10.1146/annurev.fluid.30.1.139. Crossref, Web of Science, Google Scholar
R. Danchin and B. Desjardins, Ann. Inst. Henri Poincaré Anal. Nonlin. 18(1), 97 (2001), DOI: 10.1016/S0294-1449(00)00056-1. Crossref, Web of Science, Google Scholar
F. Guillén-González, P. Damázio and M. A. Rojas-Medar, J. Math. Anal. Appl. 326, 468 (2007). Crossref, Web of Science, Google Scholar
D. J. Korteweg, Archives Nerlandaises des Sciences Exactes et naturelles, Ser. II 6, 1 (1901). Web of Science, Google Scholar
I. Kostinet al., M2AN 37, 741 (2003), DOI: 10.1051/m2an:2003042. Crossref, Google Scholar
P. L. Lions , Mathematical Topics in Fluids Mechanics, Incompressible fluids I ( Clarendon Press , 1996 ) . Google Scholar
V. A. Solonnikov, Tr. Mat. Inst. Akad. Nauk SSSR 70, 213 (1964). Google Scholar
M. Syet al., C. R. Acad. Sci. Paris Ser. I 342, 169 (2006). Crossref, Web of Science, Google Scholar