J. Korean Math. Soc. 2013; 50(4): 771-795
Printed July 1, 2013
https://doi.org/10.4134/JKMS.2013.50.4.771
Copyright © The Korean Mathematical Society.
Bum Ja Jin
Mokpo National University
In this paper we consider the Navier-Stokes equations in the half space. Our aim is to construct a mild solution for initial data in $B^{-\alpha}_{\infty,\infty}({\mathbb R}^n_+)$, $0<\alpha<1$. To do this, we derive the estimate of the Stokes flow with singular initial data in $B^{-\alpha}_{\infty,q}({\mathbb R}^n_+)$, $0<\alpha<1$, $ 1< q\leq \infty$.
Keywords: Besov space, half space, Navier-Stokes, Stokes, mild solution
MSC numbers: 35K51, 76D05
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