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Global solvability of the Navier-Stokes equations in spaces based on sum-closed frequency sets. (English) Zbl 1144.76009

Summary: We prove existence of global regular solutions for three-dimensional Navier-Stokes equations with (or without) Coriolis force for a class of initial data \(u_0\) in the space \(\text{FM}_{\sigma,\delta}\), i.e., for functions whose Fourier image \(\widehat{u}_0\) is a vector-valued Radon measure and that are supported in sum-closed frequency sets with distance \(\delta\) from the origin. In our main result we establish an upper bound for admissible initial data in terms of Reynolds number, uniform in the Coriolis parameter. In particular this means that this upper bound is linearly growing in \(\delta\). This implies that we obtain global-in-time regular solutions for large (in norm) initial data \(u_0\) which may not decay at space infinity, provided that the distance \(\delta\) of the sum-closed frequency set from the origin is sufficiently large.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
35Q30 Navier-Stokes equations
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