Stokes equations and elliptic systems with nonstandard boundary conditions (Q550429)

The incompressible Navier-Stokes equations with nonstandard boundary conditions \({\mathbf u} \cdot {\mathbf n} =0\), \(\mathrm{curl} ({\mathbf u}) \times {\mathbf u}=0\) were studied in [\textit{V. Girault}, Lect. Notes Math. 1431, 201--218 (1990; Zbl 0702.76037)]. The present paper concerns stationary Stokes equations in bounded, possibly multiple-connected domains, with similar nonhomogeneous non-standard boundary conditions. The existence and uniqueness of strong, weak and very weak solutions is proved using inf-sup conditions (based on the Necas inequality). The main contribution of the authors is to consider the above problem in non-Hilbert spaces \(L^p\).