My research interests are mostly in partial differential equations, fluid mechanics and spectral theory. Here you can find a few selected papers that illustrate my latest research interests. My full publication list is here.


3D Euler and Navier-Stokes equations: vortex structures and Beltrami fields

- A. Enciso, D. Peralta-Salas, A. Romaniega, Beltrami fields exhibit knots and chaos almost surely, preprint.
- A. Enciso, D. Peralta-Salas, F. Torres de Lizaur, Knotted structures in high-energy Beltrami fields on the torus and the sphere, Ann. Sci. Éc. Norm. Sup. 50 (2017) 995-1016.
- A. Enciso, R. Lucà, D. Peralta-Salas, Vortex reconnection in the three dimensional Navier-Stokes equations, Adv. Math. 309 (2017) 452-486.
- A. Enciso, D. Peralta-Salas, Beltrami fields with a nonconstant proportionality factor are rare, Arch. Rat. Mech. Anal. 220 (2016) 243–260.
- A. Enciso, D. Peralta-Salas, Existence of knotted vortex tubes in steady fluid flows, Acta Math. 214 (2015) 61–134.
- A. Enciso, D. Peralta-Salas, Knots and links in steady solutions of the Euler equation, Ann. of Math. 175 (2012) 345–367.

Free boundary problems for incompressible fluids and singular interfaces

- A. Enciso, J. Gómez-Serrano, B. Vergara, Uniqueness, convexity and sharp asymptotics for Whitham's highest wave, preprint.
- D. Córdoba, A. Enciso, N. Grubic, Local wellposedness for the free boundary incompressible Euler equations with interfaces that exhibit cusps and corners of nonconstant angle, preprint.
- A. Enciso, A. Luque, D. Peralta-Salas, MHD equilibria with nonconstant pressure in nondegenerate toroidal domains, preprint.
- D. Córdoba, A. Enciso, N. Grubic, Self-intersecting interfaces for stationary solutions of the two-fluid Euler equations, Ann. of PDE 7 (2021) 12.
- D. Córdoba, A. Enciso, N. Grubic, On the existence of stationary splash singularities for the Euler equations, Adv. Math. 288 (2016) 922–941.

Spectral geometry, nodal sets of eigenfunctions, random monochromatic waves

- A. Enciso, A. García-Ruiz, D. Peralta-Salas, Localization properties of high energy eigenfunctions on flat tori, preprint.
- A. Enciso, D. Peralta-Salas, A. Romaniega, Critical point asymptotics for Gaussian random waves with densities of any Sobolev regularity, preprint.
- A. Enciso, J. Gómez-Serrano, Spectral determination of semi-regular polygons, J. Differential Geom., in press.
- A. Enciso, D. Hartley, D. Peralta-Salas, A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator, J. Eur. Math. Soc. 20 (2018) 301-314.
- A. Enciso, D. Peralta-Salas, Eigenfunctions with prescribed nodal sets, J. Differential Geom. 101 (2015) 197–211.

Critical points and level sets of solutions to PDEs; global approximation theorems

- A. Enciso, D. Peralta-Salas, Approximation theorems for the Schrödinger equation and quantum vortex reconnection, Comm. Math. Phys., in press.
- A. Enciso, M.A. García-Ferrero, D. Peralta-Salas, Approximation theorems for parabolic equations and movement of hot spots, Duke Math. J. 168 (2019) 897-939.
- A. Enciso, D. Peralta-Salas, Bounded solutions to the Allen-Cahn equation with level sets of any compact topology, Anal. PDE 9 (2016) 1433–1446.
- A. Enciso, D. Peralta-Salas, Submanifolds that are level sets of a solution to an elliptic PDE, Adv. Math. 249 (2013) 204–249.
- A. Enciso, D. Peralta-Salas, Critical points of Green’s functions on complete manifolds, J. Differential Geom. 92 (2012) 1–29.
- A. Enciso, D. Peralta-Salas, Critical points and level sets in exterior boundary problems, Indiana Univ. Math. J. 58 (2009) 1947–1970.

Wave equations, Carleman estimates and anti-de Sitter spacetimes

- A. Enciso, A. Shao, B. Vergara, Robust quantitative uniqueness and controllability for parabolic equations with inverse-square potentials via non-smooth Carleman weights, preprint.
- A. Enciso, A. Shao, B. Vergara, Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials, J. Eur. Math. Soc. 23 (2021) 3459-3495.
- A. Enciso, N. Kamran, Lorentzian Einstein metrics with prescribed conformal infinity, J. Differential Geom. 112 (2019) 505-554.
- A. Enciso, N. Kamran, A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces, J. Math. Pures Appl. 103 (2015) 1053–1091.

Overdetermined elliptic boundary value problems

- M. Domínguez-Vázquez, A. Enciso, D. Peralta-Salas, Overdetermined boundary problems with non constant Dirichlet and Neumann data, preprint.
- M. Domínguez-Vázquez, A. Enciso, D. Peralta-Salas, Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems, Arch. Rat. Mech. Anal. 239 (2021) 1327-1347.
- M. Domínguez-Vázquez, A. Enciso, D. Peralta-Salas, Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities, Adv. Math. 351 (2019) 718-760.

Miscellanea

- A. Enciso, D. Peralta-Salas, A problem of Ulam about magnetic fields generated by knotted wires, Ergodic Th. Dynam. Syst. 39 (2019) 2048-2070.
- A. Enciso, M.A. García-Ferrero, D. Peralta-Salas, The Biot-Savart operator of a bounded domain, J. Math. Pures Appl. 119 (2018) 85-113.
- A. Enciso, D. Peralta-Salas, F. Torres de Lizaur, Helicity is the only integral invariant of volume-preserving transformations, Proc. Nat. Acad. Sci. 113 (2016) 2035–2040.
- A. Ballesteros, A. Enciso, F. J. Herranz, O. Ragnisco, Hamiltonian systems admitting a Runge–Lenz vector and an optimal extension of Bertrand’s theorem to curved manifolds, Comm. Math. Phys. 290 (2009) 1033–1049.