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 ∞ . Journal of Mathematical Fluid Mechanics Springer Journals

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

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Springer International Publishing
Copyright © 2016 by Springer International Publishing
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
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