Student Analysis Seminar

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Existence of non-convex V-states

Speaker: Gerard Castro-López, NYU Courant

Location: Warren Weaver Hall 512

Date: Monday, September 28, 2026, 12:30 p.m.

Synopsis:

V-states are uniformly rotating vortex patches of the 2D Euler equation. The only known explicit examples are circles and ellipses: the rest of positive existence results use local or global bifurcation arguments and don’t give any quantitative information of the solutions. In this talk I will prove the existence of solutions far from the perturbative regime, being able to extract nontrivial features of them and a precise quantitative description. The proof uses a combination of analysis and computer-assisted techniques based on interval arithmetic. This talk is based on joint work with Javier Gómez-Serrano.

Special emphasis will be placed on the general methodology of using computer-assisted proofs to construct solutions of nonlinear PDEs. This approach has recently become considerably more accessible with the emergence of AI-assisted tools.