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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.