Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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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.

Navier-Stokes equations in Besov space $B^{-s}_{\infty,\infty}({\mathbb R}^n_+)$

Bum Ja Jin

Mokpo National University

Abstract

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