2022-05-28T04:43:02Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696032018-04-25T23:44:10Zhdl_2115_45007hdl_2115_116Global solvabiliy of the Navier-Stokes equations in spaces based on sum-closed frequency setsGiga, YoshikazuInui, KatsuyaMahalov, AlexSaal, JürgenNavier-Stokes equations with rotationglobal wellposedness410We 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.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69603info:doi/10.14943/83945https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69603/1/pre795.pdfHokkaido University Preprint Series in Mathematics7951182006engpublisher