On the Oseen-Brinkman flow around an (m-1)-dimensional solid obstacle

0474335 - MÚ 2018 RIV AT eng J - Článek v odborném periodiku
Kohr, M. - Medková, Dagmar - Wendland, W. L.
On the Oseen-Brinkman flow around an (m-1)-dimensional solid obstacle.
Monatshefte für Mathematik. Roč. 183, č. 2 (2017), s. 269-302. ISSN 0026-9255. E-ISSN 1436-5081
Grant CEP: GA ČR GA16-03230S
Institucionální podpora: RVO:67985840
Klíčová slova: transmission problem * Brinkman system * Oseen system
Obor OECD: Pure mathematics
Impakt faktor: 0.735, rok: 2017
http://link.springer.com/article/10.1007/s00605-016-0981-2?wt_mc=Internal.Event.1.SEM.

The purpose of this paper is to develop a layer potential analysis in order to show the well-posedness result of a transmission problem for the Oseen and Brinkman systems in open sets with compact Lipschitz boundaries and around a lower dimensional solid obstacle, when the boundary data belong to some Lebesgue's spaces. In the tree dimensional space or if the Brinkman system is given on bounded open set then there exists a solution of the transmission problem for arbitrary data. If the Brinkman system is given on exterior open set in the plane then necessary and sufficient conditions for the existence of a solution of the transmission problem are stated. A solution of the transmission problem is not unique. All solutions of the problem are found.
Trvalý link: http://hdl.handle.net/11104/0271422