Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions

Pages: 967 - 979, Volume 7, Issue 5, October 2014      doi:10.3934/dcdss.2014.7.967

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Paul Deuring - Univ Lille Nord de France, 59000 Lille, France (email)
Stanislav Kračmar - Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35 Prague 2, Czech Republic (email)
Šárka Nečasová - Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic (email)

Abstract: We consider Leray solutions of the Oseen system with rotational terms, in an exterior domain. Such solutions are characterized by square-integrability of the gradient of the velocity and local square-integrability of the pressure. In a previous paper, we had shown a pointwise decay result for a slightly stronger type of solution. Here this result is extended to Leray solutions. We thus present a second access to this result, besides the one in G. P. Galdi, M. Kyed, Arch. Rat. Mech. Anal., 200 (2011), 21-58.

Keywords:  Stationary Oseen problem, rotating body, Leray solution, pointwise decay, representation formula.
Mathematics Subject Classification:  35Q35, 76D07, 35J57.

Received: April 2013;      Available Online: May 2014.