Time: 13:30-15:30, November 9 2026

Venue: E14-212, Yungu Campus

Speaker: Jose Antonio Lucas Manchon, Instituto de Ciencias Matematicas

Title: Finite-time blow-up for generalized SQG in the Sobolev well-posedness regime

Abstract: This is a talk about a recent work joint with D. Córdoba, O. Dominguez and L. Martinez-Zoroa, on finite-time singularities for the forced generalized SQG equation

This equation is locally well-posed in H^κ for κ > 2 + γ, also with forces in L_t^1 H^κ, but whether classical finite-energy solutions can blow up infinite time in this regime is a major open problem. We will show that, for every γ∈ (0, 1), there exist a smooth, compactly supported initial datum and a force F such that the classical solution loses H^κ regularity at t = 1, while the force remains in the well-posedness class L^1 ([0 , 1]; H^κ) up to and including the blow-up time, for some κ > 2 + γ. Hence the singularity cannot be attributed to a lack of regularity of the data or of the force.

In this talk we motivate the problem and give a complete overview of the proof: a multilayer construction in which the shear generated by the previous layers elongates each new layer at a finer scale, together with a finite hierarchy of corrections that cancels the self interaction errors.

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