A Nitsche method for incompressible fluids with general dynamic boundary conditions Gazca-Orozco, Pablo Alexei Gmeineder, Franz Maringová, Erika Tscherpel, Tabea 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 Publishing 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22718 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202526500508 info:eu-repo/semantics/altIdentifier/issn/0218-2025 info:eu-repo/semantics/altIdentifier/e-issn/1793-6314 info:eu-repo/semantics/altIdentifier/arxiv/2502.09550 info:eu-repo/semantics/openAccess