Global \(L^ n\)-solution and its decay property for the Navier-Stokes equations in half-space \(R^ n_ +\) (Q752321)

The existence and uniqueness of a global strong \(L^ n\)-solution as well as an \(L^ n\)-decay result are shown for the Navier-Stokes equations in \({\mathbb{R}}^ n_+\times (0,\infty)\) for small initial data. Compared to similar results the proof is complete and simplified. A main tool consists in the implicit function theorem which allows to conclude the \(L^ n\)-continuity of the solution with respect to the initial data.