@article{22718,
  abstract     = {Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations may occur. For a unifying framework of such relations, we present a fully discrete numerical scheme for the time-dependent Navier–Stokes equations subject to impermeability and general slip-type boundary conditions on polyhedral domains. Based on compactness arguments, we prove convergence of subsequences, finally ensuring the existence of a weak solution. The numerical scheme uses a general inf-sup stable pair of finite element spaces for the velocity and pressure, a regularisation approach for the implicit slip boundary condition and, most importantly, a general Nitsche method to impose the impermeability and a backward Euler time stepping. One of the key tools in the convergence proof is an inhomogeneous Korn inequality that includes a normal trace term.},
  author       = {Gazca-Orozco, Pablo Alexei and Gmeineder, Franz and Maringová, Erika and Tscherpel, Tabea},
  issn         = {1793-6314},
  journal      = {Mathematical Models and Methods in Applied Sciences},
  publisher    = {World Scientific Publishing},
  title        = {{A Nitsche method for incompressible fluids with general dynamic boundary conditions}},
  doi          = {10.1142/S0218202526500508},
  year         = {2026},
}