# NAVIER-STOKES EQUATIONS IN BESOV SPACE B-s∞,∞(ℝn+)

• Jin, Bum Ja (Department of Mathematics Education, Mokpo National University)
• Published : 2013.07.01
• 90 12

#### 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

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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