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# The Navier-Stokes equations with initial data in uniformly local L p spaces

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 Title: The Navier-Stokes equations with initial data in uniformly local L p spaces Authors: Maekawa, Yasunori Browse this author Terasawa, Yutaka Browse this author Issue Date: 2005 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 741 Start Page: 1 End Page: 32 Abstract: We construct the local mild solutions of the Cauchy problem for the incompressible homogeneous Navier-Stokes equations in the $d$-dimensional Eucledian space with initial data in uniformly local $L^{p}$ (=$L^{p}_{uloc}) spaces where$ p $is larger than or equal to$d$. As an application, we show that the mild solution associated with$ L^{d}_{uloc} $almost periodic initial data at time zero becomes uniformly local almost periodic (=$ L^{\infty}-almost periodic ) in any positive time. Type: bulletin (article) URI: http://hdl.handle.net/2115/69549 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics