7 papers
Hölder continuous dissipative solutions of ideal MHD with nonzero helicity
Alberto Enciso, Javier Peñafiel-Tomás, Daniel Peralta-Salas
We prove the existence of weak solutions to the 3D ideal MHD equations, of class with , for which the total energy and the cross helicity (i.e., the so-called ElsÃ…
Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity
Alberto Enciso, Manuel Garzón, Daniel Peralta-Salas
We prove that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential on exhibits an arbitrarily high number of hyperbolic pe…
Splitting and Merging of Stagnation Points of Solutions to the 2D Navier-Stokes Equations
Isidro Benaroya, Alberto Enciso, Daniel Peralta-Salas
We construct solutions to the Navier-Stokes equations on with an arbitrary number of stagnation points which merge and split along trajectories that can be prescribe…
An extension theorem for weak solutions of the 3d incompressible Euler equations and applications to singular flows
Alberto Enciso, Javier Peñafiel-Tomás, Daniel Peralta-Salas
We prove an extension theorem for local solutions of the 3d incompressible Euler equations. More precisely, we show that if a smooth vector field satisfies the Euler equations in a…
Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates
Alberto Enciso, Arick Shao, Bruno Vergara
We consider heat operators on a convex domain , with a critically singular potential that diverges as the inverse square of the distance to the boundary of . We establish a…
Local limits of high energy eigenfunctions on integrable billiards
Alberto Enciso, Alba Garcia-Ruiz, Daniel Peralta-Salas
Berry's random wave conjecture posits that high energy eigenfunctions of chaotic systems resemble random monochromatic waves at the Planck scale. One important consequence is that,…