On the hydrodynamic motion in a domain with mixed boundary conditions: Existence, uniqueness, stability and linearization principle

Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

“…They were also used in [14] for the study of the non stationary Navier-Stokes equations in half-spaces of R 3 . We finally refer to [43,44] for the study of the non stationary problem of Navier-Stokes with mixed boundary conditions that include (1.5) without friction.…”

Navier–Stokes equations with Navier boundary condition

“…Indeed, one can cite the work of V. A. Solonnikov and V. E. Ščadilov where the authors studied the Hilbert case when the data f belongs to L 2 (Ω). Another example is the work of G. Mulone and F. Salemi where authors studied the existence of weak solution in H 1 (Ω) for stationary Navier–Stokes system (the evolution system is also studied). In our works, we extend these results and the result obtained in for the case of L p ‐theory not only for large values of p but also for small values ( ).…”

On the Stokes system and on the biharmonic equation in the half‐space: an approach via weighted Sobolev spaces

“…Section 4 is devoted to Stokes system (1) with an adhesion condition (2). Existence, uniqueness and regularity are established for several kinds of behaviours at inÿnity by means of the re ection principle.…”

“…with an adhesion condition u = g at (2) or with a slip condition u · n = g; e i · T(u; p) · n = z · e i ∀i ∈ {1; : : : ; n − 1} at (3) 374 T. Z. BOULMEZAOUD where T(u; p) = −pI + (9 i u j + 9 j u i ) n i; j = 1 (4) denotes the stress tensor, n = (0; : : : ; 0; −1) is the normal vector on and e 1 ; : : : ; e n−1 are the tangential vectors on . Problem (1), (2) is obtained from Navier-Stokes equation by ignoring the non-linear convection term, while (1), (3) appears in studying free-boundary problems (see, e.g., References [1; 2]).…”

“…Stokes problem (1), (2) was studied in References [3][4][5] using homogeneous spaces. Our method here is completely di erent since, on the one hand, it rests on the use of a large class of weighted Sobolev spaces of the type…”