Blow-up results for the semilinear Schrödinger equations with forcing and gradient terms: the critical cases

The paper is devoted to the study of critical cases of the nonlinear Schrödinger (NLS) equation with source and gradient terms, subsequently providing answers to some open questions posed by Alotaibi et al in [Z. Angew. Math. Phys., 73 (2022), 1-17]. The main results state that in critical cases, the problem under consideration does not have any global-in-time weak solutions. The proof approach is based on modified method of test functions specifically adapted to the nature of considered problems.