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arXiv · 2505.12232

Global and blow-up solutions for a non-local integrable equation with applications to geometry

Nilay Duruk Mutlubas·Igor Leite Freire
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Abstract

We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wave propagation. Under a natural assumption on the initial momentum, we prove that the solution remains globally regular in arbitrary finite-order Sobolev spaces. The proof relies on an inductive energy method involving a hierarchy of functional estimates and applies to both the periodic and non-periodic settings. We determine a criterion for the existence of blow-up solutions. The consequences of these qualitative properties of the solutions on Riemannian surfaces determined by the solutions of the equation are investigated.

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Nilay Duruk Mutlubas, Igor Leite Freire. 2025-05-18. Global and blow-up solutions for a non-local integrable equation with applications to geometry. https://arxiv.org/abs/2505.12232

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