article epub_ahead yes Pablo Alexei Gazca-Orozco author Franz Gmeineder author Erika Maringová author dbabca31-66eb-11eb-963a-fb9c22c880b4 Tabea Tscherpel author JuFi department 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. World Scientific Publishing2026 eng 0218-2025 1793-6314 2502.0955010.1142/S0218202526500508 Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026. doi:<a href="https://doi.org/10.1142/S0218202526500508">10.1142/S0218202526500508</a> Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. 2026. A Nitsche method for incompressible fluids with general dynamic boundary conditions. Mathematical Models and Methods in Applied Sciences. Gazca-Orozco, P. A., Gmeineder, F., Maringová, E., &#38; Tscherpel, T. (2026). A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0218202526500508">https://doi.org/10.1142/S0218202526500508</a> P. A. Gazca-Orozco, F. Gmeineder, E. Maringová, and T. Tscherpel, “A Nitsche method for incompressible fluids with general dynamic boundary conditions,” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. Gazca-Orozco, Pablo Alexei, Franz Gmeineder, Erika Maringová, and Tabea Tscherpel. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href="https://doi.org/10.1142/S0218202526500508">https://doi.org/10.1142/S0218202526500508</a>. Gazca-Orozco, Pablo Alexei, et al. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href="https://doi.org/10.1142/S0218202526500508">10.1142/S0218202526500508</a>. P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical Models and Methods in Applied Sciences (2026). 227182026-08-16T22:01:44Z2026-08-18T07:51:59Z