We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-16,
author = {Tomasz Piasecki},
title = {Steady compressible Oseen flow with slip boundary conditions},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {247-264},
zbl = {1167.35430},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-16}
}
Tomasz Piasecki. Steady compressible Oseen flow with slip boundary conditions. Banach Center Publications, Tome 86 (2009) pp. 247-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-16/