Wednesday, April 8
3:00-3:30, PH330 Tea
3:30-4:30, PH328 Alexandru Ionescu, Lecture 1, “Water wave models in 2D and 3D: regularity and formation of singularities”
4:45-5:15, PH328 Yu Deng, “Global solutions to 3D Klein-Gordon systems”

Thursday, April 9
9:00-9:30, PH330 Tea
9:30-10:30, PH328 Alexandru Ionescu, Lecture 2, “Water wave models in 2D and 3D: regularity and formation of singularities”
Break
3:30-4:30, HN112 Alexandru Ionescu, Lecture 3, “Water wave models in 2D and 3D: regularity and formation of singularities”
4:45-5:15, HN112 Xuecheng Wang, “Global infinite energy solution for the 2D gravity water waves systems”

Friday, April 10
9:30-10:00, PH330 Tea
10:00-11:00, PH334 Alexandru Ionescu, Lecture 4, “Water wave models in 2D and 3D: regularity and formation of singularities”

Abstracts:

Alexandru Ionescu, Water wave models in 2D and 3D: regularity and formation of singularities:

I will discuss some recent work on the global regularity and the formation of singularities of several water wave models in 2 and 3 dimensions. The results concern the pure gravity model, the capillary waves equation, and the two-fluid model.

Yu Deng, Global solutions to 3D Klein-Gordon systems:

Consider a 3D quasilinear Klein-Gordon system with arbitrary speed and mass; we will prove global existence for small data, extending a previous result of Ionescu-Pausader, where a nondegeneracy condition was assumed.

Xuecheng Wang, Global infinite energy solution for the 2D gravity water waves system:

We consider the infinite depth gravity water waves system (without surface tension) in dimension two and prove the global existence and the modified scattering properties of solution for a class of initial data, which has arbitrary large energy and is small at the level above the Hamiltonian. More precisely, for the gravity water waves system, the Hamiltonian is at level $L^2\times \dot{H}^{1/2}$, we only require smallness above the level $\dot{H}^{1/5}\times \dot{H}^{1/5+1/2}$ to derive global solution.