J. Korean Math. Soc. 2012; 49(2): 315-324
Printed March 1, 2012
https://doi.org/10.4134/JKMS.2012.49.2.315
Copyright © The Korean Mathematical Society.
Namkwon Kim and Minkyu Kwak
Chosun University, Chonnam National University
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 $H^1$ and the forcing function in $L^p([0, T); L^2)$, $T>0$, $2 \leq p \leq +\infty$ satisfy a certain condition. This condition commonly 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 $\epsilon$ tends to zero.
Keywords: Navier-Stokes equations, global existence, strong solution
MSC numbers: 35Q30, 35K51
2023; 60(3): 565-586
2022; 59(3): 519-548
2020; 57(1): 215-247
2016; 53(3): 597-621
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd