Uniqueness and regularity for the Cahn-Hilliard-Hele-Shaw system with logarithmic potential
Andrea Giorgini, Università di Pavia
Sala conferenze IMATI-CNR, Pavia - Tuesday, November 28, 2017 h.15:00
Abstract. Many applications of multiphase flows in Engineering, Physics and Life Sciences involve the motion of fluids and their mutual interplay at interfaces separating immiscible components. Complex mechanisms already appear in simple experiments, such as breakup and coalescence of drops, mixing in a driven cavity and thermocapillary flow, revealing remarkable similarities with global-impact issues, like tumor growth dynamics. Understanding and modeling the transition occurring when interfaces merge and reconnect is still a major challenge in fluid mechanics.
In the last decades, diffuse interface methods have been successfully employed to describe the evolution of binary fluid mixtures as witnessed by a vast literature mostly devoted to numerical simulations. In particular, the Cahn-Hilliard-Hele-Shaw system plays a central role in multiphase flows when viscous forces prevail over the inertial ones. During the seminar I will discuss some recent results concerning uniqueness and regularity properties of weak solutions as well as the validity of the separation property in dimension two.
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