Francisco Torres de Lizaur

Research

• (with R. Cardona) Contact type solutions and non-mixing of the 3D Euler equations, Arxiv

• (with A. Enciso and D. Peralta-Salas) Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher. J. Differential Equations 354 (2023), 170–182 , Arxiv

• (with A. D Martínez) Sign equidistribution of Legendre polynomials,  Anal. Math. Phys. (2023), Arxiv

• (with A. Enciso and D. Peralta-Salas) Limiting measures and energy growth for sequences of solutions to Taubes's Seiberg-Witten equations, J Geom Anal 33, 269 (2023), Arxiv

• Chaos in the incompressible Euler equation on manifolds of high dimension, Invent. Math. (2022), Arxiv 

• (with A. D Martínez) Distribution symmetry of toral eigenfunctions, Rev. Mat. Iberoamericana (2021).

• Periodic orbits of analytic Euler fields on 3-manifolds, Arxiv

• Geometric structures in the nodal sets of eigenfunctions of the Dirac operator, Arxiv

• (with D. Peralta-Salas and A. Rechtman) A characterization of 3D steady Euler flows using commuting zero-flux homologies, Ergodic Theory Dynam. Systems 41 (2021), no. 7, 2166–2181, Arxiv

• (with A. Enciso and D. Peralta-Salas) High-energy eigenfunctions of the Laplacian on the torus and the sphere with nodal sets of complicated topology, in S. Koike ( Ed. ),  Nonlinear Partial Differential Equations for Future Applications, Singapore: Springer, Arxiv

• (with A. Enciso and D. Peralta-Salas) Helicity is the only integral invariant of volume-preserving transformations. Proc. Natl. Acad. Sci. USA 113 (2016), no. 8, 2035–2040, Arxiv

• (with A. Enciso and D. Peralta-Salas)  Knotted structures in high-energy Beltrami fields on the torus and the sphere. Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 4, 995–1016, Arxiv