Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Yang, Qixiang¹  Yang, Haibo² 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[2] Wuhan Text Univ, Coll Math & Comp, Wuhan 430200, Hubei, Peoples R China

关键词: Fractional Navier-Stokes equations;    Parameter Meyer wavelets;    Besov-Morrey spaces;    Triebel-Lizorkin-Morrey spaces;    Well-posedness;    Y spaces;   

DOI  :  10.1016/j.jde.2017.12.017

来源: Elsevier

【 摘 要 】

For fractional NavierStokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C(R+,X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y-m,Y-beta where Y-m,Y-beta is not contained in C(R+,B-infinity(1-2 beta, infinity)). Consequently, for 1/2 < beta < 1, we establish the global well-posedness of fractional NavierStokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any BesovMorrey spaces (B-p,q(gamma 1 gamma 2)(R-n))(n) or any Triebel-Lizorkin-Morrey spaces (F-p,F-q (gamma 1,gamma 2)(R-n))(n) where 1 <= p, q <= infinity,0 <= gamma 2 <= n/p, gamma 1 - gamma 2 = 1 - 2 beta. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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