On the Stokes equation with Neumann boundary condition

In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in R, which is the linearized model problem of the free boundary value problem. Mainly, we prove Lp-Lq 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.

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