The Space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 , Volumetric Sparseness, and 3D NSE

The Space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 , Volumetric Sparseness, and... In the context of the $${L^\infty}$$ L ∞ -theory of the 3D NSE, it is shown that smallness of a solution in Besov space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 suffices to prevent a possible blow-up. In particular, it is revealed that the aforementioned condition implies a particular local spatial structure of the regions of high velocity magnitude, namely, the structure of local volumetric sparseness on the scale comparable to the radius of spatial analyticity measured in $${L^\infty}$$ L ∞ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

The Space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 , Volumetric Sparseness, and 3D NSE

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-016-0288-z
Publisher site
See Article on Publisher Site

Abstract

In the context of the $${L^\infty}$$ L ∞ -theory of the 3D NSE, it is shown that smallness of a solution in Besov space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 suffices to prevent a possible blow-up. In particular, it is revealed that the aforementioned condition implies a particular local spatial structure of the regions of high velocity magnitude, namely, the structure of local volumetric sparseness on the scale comparable to the radius of spatial analyticity measured in $${L^\infty}$$ L ∞ .

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Sep 6, 2016

References

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