First boundary value problem for the Navier-Stokes equations in domains with non smooth boundaries. (English. Abridged French version) Zbl 0744.35034

Summary: It is shown that the principal facts in the theory of attractors for the Navier-Stokes equations and some other properties of these equations proved before for domains \(\Omega\) with \(C^ 2\)-boundaries \(\partial\Omega\) in fact are true for \(\Omega\) with arbitrary \(\partial\Omega\). The proof is based on two new a priori estimates. These estimates hold also for various approximations of the Navier-Stokes equations.


35Q30 Navier-Stokes equations
35B45 A priori estimates in context of PDEs