The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains. (Q636996)

The authors investigate the Navier-Stokes equations in a three-dimensional bounded Lipschitz domain \(\Omega \), equipped with ``free boundary'' conditions. Applying the Fujita-Kato method they prove the existence of a local mild solution. The free boundary conditions means that the following boundary condition \(\nu \cdot u=0\) and \(\nu \times \operatorname {curl} u = 0\), where \(\nu \) is the outward unit normal to \(\Omega \) and \(u\) is the velocity field. The approach uses the properties of the Hodge-Laplacian in Lipschitz domain.