The HADES seminar on Tuesday, November 18th, will be at 3:30pm in Room 740.

Speaker: Xilu Zhu

Abstract: We explore the long-time behavior of multispeed Klein–Gordon systems in space dimension two. In terms of Klein–Gordon systems, the space dimension two is somehow considered as a critical threshold with possible transition from stability to instability. To illustrate this, we first prove a global well-posedness result when Klein–Gordon systems satisfy Ionescu–Pausader non-degeneracy conditions and the nonlinearity is assumed to be semilinear. Second, on the other hand, we construct a specific Klein–Gordon system such that one of the nondegeneracy conditions is violated and its solution has an infinite time blowup, which implies a type of ill-posedness.