Journal of Mathematical Fluid Mechanics

, Volume 2, Issue 2, pp 151–184

# Isolated Singularity for the Stationary Navier—Stokes System

• H. J. Choe
• H. Kim

DOI: 10.1007/PL00000951

Cite this article as:
Choe, H. & Kim, H. J. math. fluid mech. (2000) 2: 151. doi:10.1007/PL00000951

## Abstract.

In this paper the classical method to prove a removable singularity theorem for harmonic functions near an isolated singular point is extended to solutions to the stationary Stokes and Navier—Stokes system. Finding series expansion of solutions in terms of homogeneous harmonic polynomials, we establish some known results and new theorems concerning the behavior of solutions near an isolated singular point. In particular, we prove that if (u, p) is a solution to the Navier—Stokes system in $$B_R \setminus \{0\}$$, $$n \geq 3$$ and $$|u(x)| = o\,(|x|^{-(n - 1)/2})$$ as $$|x| \to 0$$ or $$u \in L^{2n/(n - 1)}(B_R)$$, then (u, p) is a distribution solution and if in addition, $$u \in L^{\beta}(B_R)$$ for some $$\beta > n$$ then ( u, p) is smooth in BR.

Keywords. The stationary Navier—Stokes system, homogeneous harmonic polynomials, power series expansion and isolated singularity.

## Copyright information

© Birkhäuser Verlag, Basel, 2000

## Authors and Affiliations

• H. J. Choe
• 1
• H. Kim
• 2
1. 1.Department of Mathematics, KAIST, Taejon, 305-701, Republic of Korea, e-mail: ch@math.kaist.ac.krKR
2. 2.Department of Mathematics, POSTECH, Pohang, 790-784, Republic of KoreaKR