Global stability for the fractional Navier‐Stokes equations in the Fourier‐Herz space | Zendy

Chen Jing | Zendy; Song Changming | Zendy

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Global stability for the fractional Navier‐Stokes equations in the Fourier‐Herz space

Author(s) -

Chen Jing,

Song Changming

Publication year - 2018

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4856

Subject(s) - mathematics , fourier transform , mathematical analysis , norm (philosophy) , perturbation (astronomy) , compressibility , stability (learning theory) , fourier series , fourier analysis , space (punctuation) , physics , mechanics , linguistics , philosophy , quantum mechanics , machine learning , political science , computer science , law

We consider global stability for the fractional incompressible Navier‐Stokes equations in a 3‐D critical Fourier‐Herz space. By introducing a weighted norm space and using Fourier localization technique, the stability of mild solutions with small initial FB ˙p , q 4 − α − 3 p( R 3 ) perturbation is established. With the Friedrichs method, the stability of weak solutions is proved under arbitrary large initial L 2 ( R 3 ) perturbation.

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