Finite time blowup for Klein‐Gordon‐Schrödinger system.

We investigate the blowup solutions to the Klein‐Gordon‐Schrödinger (KGS) system with power nonlinearity in spatial dimensions RN (N ≥ 2). Relying on a Lyapunov functional, we establish a perturbed virial‐type identity and prove the existence of blowup solutions for the system with a negative energy and small mass. Moreover, we obtain a new finite‐time blowup result of solutions to KGS system in the energy space by constructing a differential inequality. [ABSTRACT FROM AUTHOR]