Speaker
Description
We establish the local well-posedness of strong solutions for a thermodynamically consistent diffuse interface model describing two-phase flows with surfactants, specifically the so-called Model C introduced by Garcke, Lam, and Stinner. The highly non-standard, mixed-order strongly coupled structure of Model C invalidates the classical Agmon-Douglis-Nirenberg theory and conventional Lopatinskii-Shapiro boundary conditions due to divergent scaling behaviors. To overcome this, we develop a tailored resolvent analysis by introducing an augmented source term. Furthermore, we introduce and analyze a structural variant, denoted as Model D, which achieves a crucial structural decoupling by transferring the interfacial surfactant energy entirely from the gradient part to the potential part, and we readily establish its maximal $L^p$-regularity.