@article{d97a119446bb4b978c739d43885abc43,
title = "Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data",
abstract = "Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying kv(t)k2 → 0 as t → ∞, and determine an upper bound for the decay rate.",
keywords = "Asymptotic behaviour, Bounded domain, Exterior domain, Instationary navier-stokes equations, Nonzero boundary values, Time-dependent data, Weak solutions",
author = "Reinhard Farwig and Hideo Kozono and David Wegmann",
note = "Funding Information: Acknowledgements. The first and third authors greatly acknowledge the support of the EU Project FLUX, International Research Staff Exchange Scheme, FP7-PEOPLE-2011-IRSES. The second author was supported by the International Research Training Group (IRTG 1529) on Mathematical Fluid Dynamics, funded by Deutsche Forschungsgemeinschaft and the Japan Society for Promotion of Science.",
year = "2017",
doi = "10.1512/iumj.2017.66.6163",
language = "English",
volume = "66",
pages = "2169--2185",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "6",
}