Research

Problems and perspectives

The systems I study describe fluids, elastic structures, and interfaces whose motion is coupled to the surrounding continuum. A recurring question is how to construct solutions with sufficient control to justify changes of scale or transitions between mathematical models.

My interests include free boundary problems, two-phase flows, fluid–structure interaction, complex fluids, and moving contact lines.

Two-phase flows & singular limits

Diffuse-interface models, incompressible limits, and the passage from phase fields to sharp interfaces.

I study the well-posedness of diffuse-interface models for two-phase flows and the limits connecting different descriptions of fluid motion. My work includes quasi-incompressible Navier–Stokes/Cahn–Hilliard systems, low Mach number limits, and the sharp interface limit of Navier–Stokes/Allen–Cahn systems.

• Existence of weak and strong solutions for quasi-incompressible two-phase flows.
• Unmatched densities and singular free-energy potentials.
• Incompressible limits and higher order convergence to sharp interface models.

Fluid–structure interaction

Well-posedness and singular limits for coupled fluid and elastic structure systems.

My research on fluid–structure interaction concerns the analysis of coupled fluid and solid equations, with particular attention to well-posedness, interface conditions, and singular limits. This includes models for plaque growth and compressible fluid–structure interaction with slip boundary conditions.

• Local existence for fluid–structure interaction problems with growth.
• Quasi-stationary models and the role of domain geometry.
• Weak solutions and singular limits for compressible fluid–structure interaction.

Free boundaries & complex fluids

Moving contact lines, bulk–surface interaction, and incompressible viscoelastic two-phase flows.

I am interested in fluid models with evolving domains and interfaces, and in the coupling of fluid motion to additional material effects. My work includes thermodynamically consistent models with bulk–surface interaction and moving contact lines, as well as diffuse-interface descriptions of incompressible viscoelastic two-phase flows.

• Thermodynamic consistency of free boundary models.
• Bulk–surface material exchange and contact line motion.
• Coupling phase separation, fluid motion, and viscoelastic effects.