Blow-up for a wave equation with Hartree-type nonlinearity

Abstract This study establishes a systematic theoretical framework for blow-up dynamics of wave equations with Hartree-type nonlinearity in bounded domains. Building upon existing results on blow-up criteria under subcritical and critical initial energy levels, three fundamental advancements are achieved: First, an improved energy estimation method enables the quantitative derivation of upper bounds for blow-up time in both subcritical and critical initial energy regimes. Second, the existence of blow-up solutions is rigorously proven for arbitrary initial energy levels, particularly resolving the long-standing challenge of the existence of blow-up solutions in supercritical initial energy regime. Third, universal temporal lower bounds and rate estimation principles are revealed for all blow-up solutions, thereby comprehensively characterizing the blow-up dynamics across different energy hierarchies. These results establish a unified approach for blow-up dynamics in nonlocal wave equations.