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Global large solutions to incompressible Navier‐Stokes equations with gravity
Author(s) -
Peng Weimin,
Zhou Yi
Publication year - 2014
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.3088
Subject(s) - mathematics , navier–stokes equations , compressibility , vorticity , domain (mathematical analysis) , mathematical analysis , term (time) , space (punctuation) , vector field , pressure correction method , gravitational field , classical mechanics , physics , vortex , mechanics , geometry , quantum mechanics , linguistics , philosophy
In this per, we consider a special class of initial data for the three‐dimensional incompressible Navier–Stokes equations with gravity. We show that, under such conditions, the incompressible Navier‐Stokes equations with gravity are globally well posed, and the velocity minus gravity term has finite energy. The important features of the initial data is that the velocity fields minus gravity term are almost parallel to the corresponding vorticity fields in a very large space domain. Copyright © 2014 John Wiley & Sons, Ltd.