Abstract:

In this talk, 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 form stability to instability. To illustrate this, we first prove a global well-posedness result when Klein-Gordon systems satisfy Ionescu-Pausader nondegeneracy 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.