On the Stokes equation with Neumann boundary condition
Volume 70 / 2005
Banach Center Publications 70 (2005), 239-250
MSC: 6D07, 35Q30.
DOI: 10.4064/bc70-0-15
Abstract
In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in $\mathbb R^n$, which is the linearized model problem of the free boundary value problem. Mainly, we prove $L_p$-$L_q$ estimates for the semigroup of the Stokes operator. Comparing with the non-slip boundary condition case, we have the better decay estimate for the gradient of the semigroup in the exterior domain case because of the null force at the boundary.
