Maximal $L_1$-regularity of the Navier-Stokes equations with free boundary conditions via a generalized semigroup theory

Yoshihiro Shibata, Keiichi Watanabe

This paper develops a new approach to show the maximal regularity theorem of the Stokes equations with free boundary conditions in the half-space ${\mathbb{R}}_{+}^d$, $d\ge 2$, within…