From Strong to Very Weak Solutions to the Stokes System with Navier Boundary Conditions in the Half-Space
Chérif Amrouche, Šárka Nečasová, Yves Raudin · SIAM Journal on Mathematical Analysis · 2009
We consider the Stokes problem with slip-type boundary conditions in the half-space $\mathbb{R}^n_+$, with $n\geqslant2$. The weighted Sobolev spaces yield the functional framework. We first study generalized and strong solutions and then the case with very low regularity of data on the boundary. We apply the method of decomposition introduced in our previous work [J. Differential Equations, 244 (2008), pp. 887–915] where it is necessary to solve particular problems for harmonic and biharmonic operators with very weak data. We also envisage a wide class of behaviors at infinity for data and solutions.