@article{fad257c197a94ffb97081fe02e570576,
title = "On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces",
abstract = "This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.",
keywords = "Besov space, Homogeneous Besov space, Infinite layer, Poiseuille flow, Sobolev space, Stationary problem, Stokes equation",
author = "Takayuki Abe and Masao Yamazaki",
note = "Funding Information: ∗Partly supported by the Grant-in-Aid for Young Scientists (B) 17740072, The Ministry of Education, Culture, Sports, Science and Technology, Japan. †Partly supported by the Grant-in-Aid for Scientific Research (C) 17540174, Japan Society for the Promotion of Science.",
year = "2010",
month = mar,
doi = "10.1007/s00021-008-0276-z",
language = "English",
volume = "12",
pages = "61--100",
journal = "Journal of Mathematical Fluid Mechanics",
issn = "1422-6928",
publisher = "Birkhauser Verlag Basel",
number = "1",
}