A Lipschitz semigroup approach to two-dimensional Navier–Stokes equations

Motivated by the notion of integral solutions in the sense of Bénilan, a dissipative condition combined with a tangential condition is introduced. A generation problem of semigroups of Lipschitz operators is discussed under such a dissipative condition and the result is applied to the initial–boundary value problem for the Navier–Stokes equation in two-dimensional space.