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Explore a mathematical lecture on fluid dynamics modeling that introduces a coupled system for analyzing the flow of two incompressible, viscous, and immiscible fluids with unmatched densities and viscosities in bounded domains. Learn about the Navier-Stokes/Mullins-Sekerka system derived from the asymptotic limit of the diffuse interface model by Abels, Garcke, and Grün (2012), and discover a novel notion of weak solutions that addresses previously unresolved challenges in fluid flow analysis. Examine the global existence proof for these weak solutions and understand the consistency results that accompany this mathematical framework. Gain insights into how this new solution concept enables the inclusion of different fluid densities, incorporates a sharp energy dissipation principle following De Giorgi's approach, and provides a weak formulation for the constant contact angle condition at boundaries - all significant advances over the previous solution framework proposed by Abels and Röger in 2009. Understand the collaborative research methodology and theoretical foundations underlying this joint mathematical project with H. Abels, presented as part of the Free Boundary Problems thematic programme.
