Global Regularity and Uniqueness for a Class of Vector Triad Models via Intrinsic Geometric Frustration

This paper establishes global existence, uniqueness, and continuous dependence on initial data for a broad class of vector triad models generalising the L’vov shell model. As stated in the abstract, “the key ingredient is an intrinsic geometric frustration estimate, which shows that the nonlinear term always lies in the complex span of the interacting shells,” and “no external forcing or special initial conditions are required.” The cross-product structure of the nonlinearity prevents coherent forward energy transfer, ensuring that solutions remain globally regular. This result provides a rigorous mathematical foundation for earlier numerical observations showing that geometric frustration suppresses finite-time blow-up in vector triad models.