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Abstract:
Convection in multi-layered porous media involves complex coupling across interfaces. We investigate this by treating the classical sharp-interface model as the singular limit of a diffuse-interface formulation with smoothly varying material properties. Under constant porosity, we establish that as the transition-layer thickness vanishes, diffuse-model solutions converge to those of the sharp-interface system over finite time intervals. This analysis characterizes the formation of velocity boundary layers using delicate estimates for operators with nearly discontinuous coefficients.
For the long-time dynamics, we establish the existence of global attractors and prove their upper semicontinuity in the vanishing-layer limit. A key technical novelty is the formulation of a phase space based on fractional powers of the principal second-order elliptic operators. We establish the equivalence between these spaces with constants independent of the transition-layer thickness, enabling uniform estimates for both models. These results provide a rigorous foundation for standard interfacial conditions and offer new insights into numerical methods for layered porous structures.
Joint work with Hongjie Dong (Brown University), Kaijian Sha (EIT), and Hao Wu (Fudan).
Biography:
Xiaoming Wang is a Founding Chair Professor at the Eastern Institute of Technology. He holds a Ph.D. from Indiana University Bloomington and completed postdoctoral research at the Courant Institute. His career includes tenured faculty roles at Florida State University, Fudan University, SUSTech, and as the Havener Endowed Chair at Missouri S&T. An expert in fluid dynamics and geophysical flows, Professor Wang utilizes partial differential equations, dynamical systems, and scientific computing to solve problems in groundwater modeling and climate change. His research is dedicated to providing rigorous mathematical foundations for complex physical phenomena.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.
