# On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain

Rieko Shimada; Norikazu Yamaguchi

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 457-470
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topRieko Shimada, and Norikazu Yamaguchi. "On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain." Banach Center Publications 81.1 (2008): 457-470. <http://eudml.org/doc/281639>.

@article{RiekoShimada2008,

abstract = {This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of $L^\{p\} - L^\{q\}$ estimates for the Stokes semigroup associated with a linearized problem, which is also discussed. In particular, we mainly discuss the local energy decay property of the semigroup which is a key estimate to prove the $L^\{p\} - L^\{q\}$ estimates in an exterior domain.},

author = {Rieko Shimada, Norikazu Yamaguchi},

journal = {Banach Center Publications},

keywords = {Navier-Stokes equations; free slip boundary condition; exterior domain; local energy decay},

language = {eng},

number = {1},

pages = {457-470},

title = {On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain},

url = {http://eudml.org/doc/281639},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Rieko Shimada

AU - Norikazu Yamaguchi

TI - On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 457

EP - 470

AB - This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of $L^{p} - L^{q}$ estimates for the Stokes semigroup associated with a linearized problem, which is also discussed. In particular, we mainly discuss the local energy decay property of the semigroup which is a key estimate to prove the $L^{p} - L^{q}$ estimates in an exterior domain.

LA - eng

KW - Navier-Stokes equations; free slip boundary condition; exterior domain; local energy decay

UR - http://eudml.org/doc/281639

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.