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A class of solutions of the Navier–Stokes equations with large data

Authors :
Walter Rusin
Mohammed Ziane
Igor Kukavica
Source :
Journal of Differential Equations. 255:1492-1514
Publication Year :
2013
Publisher :
Elsevier BV, 2013.

Abstract

We are concerned with global regularity of solutions in a periodic domain Q=[0,1]3. We prove that, in the class of solutions oscillating in the vertical direction, the solutions are smooth under natural conditions on the horizontal derivatives of the horizontal components of the velocity, the derivative in the vertical direction and the vertical average of the initial data. The obtained conditions admit data whose BMO−1-norm has algebraic dependence on 1/h where h is the period of oscillation and generate global solutions. Also, the results allow non-zero force and large data which do not decay in time.

Details

ISSN :
00220396
Volume :
255
Database :
OpenAIRE
Journal :
Journal of Differential Equations
Accession number :
edsair.doi...........5f765411a027ec7eab31fd4fb34a26ab
Full Text :
https://doi.org/10.1016/j.jde.2013.05.009