Ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space near BMO−1
By Tsuyoshi Yoneda. 2010
151 citations recorded by the source corpus.
Abstract The ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space which is smaller than B ∞ , q − 1 ( q > 2 ) is considered. In 2008, Bourgain–Pavlovic proved that the 3D-Navier–Stokes equation is ill-posed in B ∞ , ∞ − 1 by showing norm inflation phenomena of the solution for some initial data. On the other hand, in 2008, Germain proved that the flow map is not C 2 in the space B ∞ , q − 1 for q > 2 . However he did not treat ill-posed problem in such spaces. Thus our result is an extension of these previous results.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/71c3151896229c0ffdd50b0d97e6fe2c608242c8
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- The Navier-Stokes equations and weak Herz spaces (2011, unknown): “Recently, in [49] he showed the ill-posedness in Ḃ−1 ∞,q for q ∈ (2,∞).”
- Well‐posedness for fractional Navier–Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn) (2012, background): “This result is later generalized by Yoneda [18] to a generalized Besov space, which is smaller than P B 1 1,q for all q > 2.”
- A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “For example, in [102], Yoneda considered the following norm.”