Igor Kukavica, Department of Mathematics, University of Southern California, Los Angeles, CA 90089; e-mail: kukavica@usc.edu

Linfeng Li, Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095; e-mail: lli265@math.ucla.edu

Amjad Tuffaha, Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE; e-mail: atufaha@aus.edu

Abstract/Résumé:

We provide a maximal regularity theorem for the linear Stokes equation with a non-homogeneous divergence condition in a bounded domain \(\Omega \subseteq \mathbb{R}^3\) and with the Neumann boundary conditions. We prove the existence and uniqueness of solutions such that the velocity belongs to the space \(H^{(s+1)/2,s+1}((0,T) \times \Omega)\), where \(s\in [1, 1.5 )\cup (1.5, 2)\).

Nous fournissons un théorème de régularité maximale pour l’équation linéaire de Stokes avec une condition de divergence non homogène dans un domaine borné \(\Omega \subseteq \mathbb{R}^3\) et avec les conditions aux limites de Neumann. On prouve l’existence et l’unicité de solutions telles que la vitesse appartient à l’espace \(H^{(s+1)/2,s+1}((0,T) \times \Omega)\), où \(s\in [1, 1.5 )\cup (1.5, 2)\).

Keywords: Local existence, Navier-Stokes equations, maximal regularity, trace regularity

AMS Subject Classification: , , Smoothness and regularity of solutions of PDE 35-11, 35A01, 35B65

PDF(click to download): Maximal regularity for the Neumann-Stokes problem in $H^{r/2,r}$ spaces