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http://dx.doi.org/10.12941/jksiam.2011.15.2.143

GLOBAL EXISTENCE FOR 3D NAVIER-STOKES EQUATIONS IN A THIN PERIODIC DOMAIN  

Kwak, Min-Kyu (DEPARTMENT OF MATHEMATICS, CHONNAM NATIONAL UNIVERSITY)
Kim, Nam-Kwon (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.15, no.2, 2011 , pp. 143-150 More about this Journal
Abstract
We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a thin periodic domain. We present a simple proof that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$(0,${\infty}$;$L^2$), $2{\leq}p{\leq}{\infty}$ satisfy certain condition. This condition is basically similar to that by Iftimie and Raugel[7], which covers larger and larger initial data and forcing functions as the thickness of the domain ${\epsilon}$ tends to zero.
Keywords
Navier-Stokes equations; global existence; strong solution;
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