We propose a structural mechanism by which finite-time blow-up in nonlinear dissipative systems may be suppressed through the formation of localized defect structures and nonlinear transport. We consider a class of coupled systems in which a fluid-type variable interacts with a curvature-generating field, giving rise to an interaction load associated with noncommutativity. Rather than directly producing global norm divergence, this load induces a transition in the effective transport coefficient once a critical threshold is exceeded. Beyond this threshold, transport is strongly enhanced, redistributing concentrated energy and inhibiting further local amplification. To formalize this mechanism, we introduce a continuum condensation–transition equation for the interaction load, incorporating nonlinear saturation and transport effects. This equation captures a structural transition from localized concentration to a transport-dominated regime when a critical scale is reached. These results suggest that blow-up in nonlinear dissipative PDEs may be reinterpreted not as unbounded growth, but as a transition from local concentration to defect-mediated transport, providing a unified perspective that links energy concentration, noncommutative structure, and large-scale redistribution dynamics.
Building similarity graph...
Analyzing shared references across papers
Loading...
Jeong Min Yeon
Korea Aerospace University
Building similarity graph...
Analyzing shared references across papers
Loading...
Jeong Min Yeon (Mon,) studied this question.
www.synapsesocial.com/papers/69ccb7b016edfba7beb89bbc — DOI: https://doi.org/10.5281/zenodo.19334968