Generalized dissipative weak solutions for incompressible non-Newtonian fluids with dynamic boundary conditions
Xin Li, Luping Wang, Yang LiuAbstract
We propose a new class of generalized dissipative weak solutions for an incompressible non-Newtonian fluid with dynamic boundary conditions. What sets the formulation apart is its inclusion of both an interior concentration measure and boundary defect measures, which collectively track compactness failures in the nonlinear stress, the boundary response, and the boundary dissipation. Existence is proved via a Galerkin scheme combined with Moreau–Yosida regularization and compactness arguments. As a final step, a relative-energy argument delivers a weak–strong uniqueness principle: every generalized dissipative weak solution emanating from given initial data agrees with the strong solution issuing from the same data, whenever the latter remains well defined.