On a generalized resolvent estimate for the Stokes system with Robin boundary condition
SHIBATA, Yoshihiro ; SHIMADA, Rieko
J. Math. Soc. Japan, Tome 59 (2007) no. 1, p. 469-519 / Harvested from Project Euclid
We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the $L_q$ framework $(1 < q < \infty)$ in a domain of $\bm{R}^n$ ( $n \geq 2$ ) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: $\nu\cdot u=0$ and $\alpha u + \beta(T(u,p)\nu - \nu) = h$ on the boundary of the domain with $\alpha, \beta \geq 0$ and $\alpha + \beta = 1$ , where $u$ denotes a velocity vector, $p$ a pressure, $T(u, p)$ the stress tensor for the Stokes flow, and $\nu$ the unit outer normal to the boundary of the domain. It presents the slip condition when $\beta =1$ and the non-slip one when $\alpha = 1$ , respectively.
Publié le : 2007-04-14
Classification:  Robin boundary condition,  Stokes system,  resolvent estimate,  35Q30,  76D07
@article{1191247596,
     author = {SHIBATA, Yoshihiro and SHIMADA, Rieko},
     title = {On a generalized resolvent estimate for the Stokes system with Robin boundary condition},
     journal = {J. Math. Soc. Japan},
     volume = {59},
     number = {1},
     year = {2007},
     pages = { 469-519},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1191247596}
}
SHIBATA, Yoshihiro; SHIMADA, Rieko. On a generalized resolvent estimate for the Stokes system with Robin boundary condition. J. Math. Soc. Japan, Tome 59 (2007) no. 1, pp.  469-519. http://gdmltest.u-ga.fr/item/1191247596/