7 papers · 1 filter
Piecewise smooth stationary Euler flows with support in a neighborhood of a helix
Daniel Peralta-Salas, Jie Wan
We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewis…
A symmetry theorem for localizable steady solutions of the 3D Euler equations
Daniel Peralta-Salas, Radu Slobodeanu
A steady Euler flow is localizable if the pressure function is constant along its stream lines. This property was used by Gavrilov to construct the first smooth compactly supported…
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…
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…
Steady 3d Euler flows via a topology-preserving convex integration scheme
Alberto Enciso, Javier Peñafiel-Tomás, Daniel Peralta-Salas
Given any smooth solenoidal vector field on , we show the existence of infinitely many Hölder-continuous steady Euler flows with the same topology as ,…