About Alexandru D. Ionescu's Work
Most of my work is concerned with questions related to the long-term dynamics of solutions of partial differential equations. These equations describe physical phenomena, such as water waves, plasma evolutions, and gravitation, and their relevance is often verified numerically. Ionescu studies the solutions of these equations rigorously, and recovers quantitative and qualitative information about their behavior, as mathematical theorems. More precisely, in recent work, my collaborators and I have considered water-wave models in dimensions 2 and 3, the more general case of two-fluid interfaces, and the Einstein–Klein–Gordon system of General Relativity. The main theorems have to do with the global stability of the equilibrium solutions of these equations, and with the construction of solutions that develop singularities in finite time.