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

Erratum to: The Space $${B^{-1}_{\infty, \infty}}$$ B ∞ , ∞ - 1 , Volumetric... J. Math. Fluid Mech. 19 (2017), 525–527 2016 Springer International Publishing Journal of Mathematical 1422-6928/17/030525-3 DOI 10.1007/s00021-016-0295-0 Fluid Mechanics ERRATUM −1 Erratum to: The Space B , Volumetric Sparseness, and 3D NSE ∞,∞ Aseel Farhat, Zoran Gruji´ c and Keith Leitmeyer Erratum to: J. Math. Fluid Mech. DOI 10.1007/s00021-016-0288-z The proof of Lemma 3.3 presented in the paper contains an error. Here, we prove a slightly diﬀerent form of the lemma that suﬃces for our purposes. In fact, this is exactly what is needed to prove the main result, Theorem 1.1. 1. The Correct Form of Lemma 3.3 The following lemma is a vector-valued, Besov space version of a scalar-valued, Sobolev space lemma in [2]. All the norms to appear in the statement of the lemma are ∞-type norms. Lemma 3.3. Let  ∈ (0, 1],r ∈ (0, 1] and u a vector-valued function in L . Then, for any pair λ, δ, λ ∈ (0, 1) and δ ∈ ( , 1), there exists an explicit constant c = c(λ, δ) such that if 1+λ u −ε ≤ c(λ, δ) r u , B ∞ ∞,∞ i,± then each of the six super-level sets A := x ∈ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

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

, Volume 19 (3) – Sep 28, 2016
3 pages

/lp/springer_journal/erratum-to-the-space-b-1-infty-infty-b-1-volumetric-sparseness-and-3d-OdXNLUqvs6
Publisher
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/s00021-016-0295-0
Publisher site
See Article on Publisher Site

### Abstract

J. Math. Fluid Mech. 19 (2017), 525–527 2016 Springer International Publishing Journal of Mathematical 1422-6928/17/030525-3 DOI 10.1007/s00021-016-0295-0 Fluid Mechanics ERRATUM −1 Erratum to: The Space B , Volumetric Sparseness, and 3D NSE ∞,∞ Aseel Farhat, Zoran Gruji´ c and Keith Leitmeyer Erratum to: J. Math. Fluid Mech. DOI 10.1007/s00021-016-0288-z The proof of Lemma 3.3 presented in the paper contains an error. Here, we prove a slightly diﬀerent form of the lemma that suﬃces for our purposes. In fact, this is exactly what is needed to prove the main result, Theorem 1.1. 1. The Correct Form of Lemma 3.3 The following lemma is a vector-valued, Besov space version of a scalar-valued, Sobolev space lemma in [2]. All the norms to appear in the statement of the lemma are ∞-type norms. Lemma 3.3. Let  ∈ (0, 1],r ∈ (0, 1] and u a vector-valued function in L . Then, for any pair λ, δ, λ ∈ (0, 1) and δ ∈ ( , 1), there exists an explicit constant c = c(λ, δ) such that if 1+λ u −ε ≤ c(λ, δ) r u , B ∞ ∞,∞ i,± then each of the six super-level sets A := x ∈

### Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Sep 28, 2016

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