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Global solvabiliy of the Navier-Stokes equations in spaces based on sum-closed frequency sets

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83945

Title: Global solvabiliy of the Navier-Stokes equations in spaces based on sum-closed frequency sets
Authors: Giga, Yoshikazu Browse this author
Inui, Katsuya Browse this author
Mahalov, Alex Browse this author
Saal,Jürgen Browse this author
Keywords: Navier-Stokes equations with rotation
global wellposedness
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 795
Start Page: 1
End Page: 18
Abstract: We prove existence of global regular solutions for the 3D Navier-Stokes quations with (or without) Coriolis force for a class of initial data u0 in he space FM¾;± , i.e. for functions whose Fourier image bu0 is a vector-valued adon measure and that are supported in sum-closed frequency sets with istance ± from the origin. In our main result we establish an upper bound or admissible initial data in terms of the Reynolds number, uniform on the oriolis parameter ­. In particular this means that this upper bound is inearly growing in ±. This implies that we obtain global in time regular olutions for large (in norm) initial data u0 which may not decay at space nfinity, provided that the distance ± of the sum-closed frequency set from he origin is sufficiently large.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69603
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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