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

Rieko 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 -