## Journal of the Mathematical Society of Japan

### On the $L_{q}-L_{r}$ estimates of the Stokes semigroup in a two dimensional exterior domain

#### Abstract

We proved $L_{q}-L_{r}$ type estimates of the Stokes semigroup in a two dimensional exterior domain. Our proof is based on the local energy decay estimate obtained by investigation of the asymptotic behavior of the resolvent of the Stokes operator near the origin.

#### Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 181-207.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213108357

Digital Object Identifier
doi:10.2969/jmsj/05110181

Mathematical Reviews number (MathSciNet)
MR1661048

Zentralblatt MATH identifier
0924.35094

Subjects
DAN, Wakako; SHIBATA, Yoshihiro. On the $L_{q}-L_{r}$ estimates of the Stokes semigroup in a two dimensional exterior domain. J. Math. Soc. Japan 51 (1999), no. 1, 181--207. doi:10.2969/jmsj/05110181. https://projecteuclid.org/euclid.jmsj/1213108357