Dynamical behavior for the solutions of the Navier-Stokes equation

Kuijie Li, Tohru Ozawa, Baoxiang Wang

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We study several quantitative properties of solutions to the incompressible Navier-Stokes equation in three and higher dimensions: (Equation Presented) More precisely, for the blow up mild solutions with initial data in L(ℝRd) and Hd/2-1(ℝd), we obtain a concentration phenomenon and blowup profile decomposition respectively. On the other hand, if the Fourier support has the form supp u0 ⊂ {ξ ∈ ℝn : ξ1 ≥ L} and ||u0|| ≪ L for some L > 0, then (1) has a unique global solution u ∈ C(ℝR+;L). In 3D, we show the compactness of the set consisting of minimal-Lp singularity-generating initial data with 3 < p < 1, furthermore, if the mild solution with data in Lp(ℝ3) blows up in a Type-I manner, we prove the existence of a blowup solution which is uniformly bounded in critical Besov spaces B-1+6/pp/2,∞ (ℝ3).

本文言語English
ページ(範囲)1511-1560
ページ数50
ジャーナルCommunications on Pure and Applied Analysis
17
4
DOI
出版ステータスPublished - 2018 7

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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