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

Title & Authors
GLOBAL EXISTENCE FOR 3D NAVIER-STOKES EQUATIONS IN A LONG PERIODIC DOMAIN
Kim, Nam-Kwon; Kwak, Min-Kyu;

Abstract
We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $\small{H^1}$ and the forcing function in $\small{L^p}$([0; T);$\small{L^2}$), T > 0, $\small{2{\leq}p{\leq}+\infty}$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\small{\epsilon}$ tends to zero.
Keywords
Navier-Stokes equations;global existence;strong solution;
Language
English
Cited by
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