Dynamical behavior for the solutions of the Navier-Stokes equation

Kuijie Li, Tohru Ozawa, Baoxiang Wang

    研究成果: Article

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    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/p p/2,∞ (ℝ3).

    元の言語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
    発行部数4
    DOI
    出版物ステータスPublished - 2018 7 1

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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