8 citations · 14 across the 9 of their papers we have counts for
10 papers
Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation
Giacomo Del Nin, Daniel Faraco, Sauli Lindberg +1
For any smooth bounded domain , we construct a divergence-free velocity field for all , and magnetic fields $B^ε\in L_t^…
Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
Francisco Mengual, Marcos Solera
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique - energy solutions below the Miura-Ju class. In particular, t…
Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation
Ángel Castro, Daniel Faraco, Francisco Mengual +1
We prove non-uniqueness of weak solutions to the forced -SQG equation with Sobolev regularity in the supercritical regime , covering the 2D Euler e…
A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation
Ángel Castro, Daniel Faraco, Francisco Mengual +1
We give a simpler proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation in the vorticity class with . The main simplification is an alt…
Dissipative Euler flows originating from circular vortex filaments
Francisco Gancedo, Antonio Hidalgo-Torné, Francisco Mengual
In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in $C([0,T],L^{2^-}…
Non-uniqueness of admissible solutions for the 2D Euler equation with vortex data
Francisco Mengual
For any we prove that there exists an initial velocity field with vorticity for which there are infinitely many bounded admis…
Localized mixing zone for Muskat bubbles and turned interfaces
Ángel Castro, Daniel Faraco, Francisco Mengual
We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in the partially unstable regime. In particular, we consider bubble and tur…
Dissipative Euler flows for vortex sheet initial data without distinguished sign
Francisco Mengual, László Székelyhidi
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a sim…
H-principle for the 2D incompressible porous media equation with viscosity jump
Francisco Mengual
In this work we extend the results in [6,32] on the 2D IPM system with constant viscosity (Atwood number ) to the case of viscosity jump (). We prove a h-principle…
Degraded mixing solutions for the Muskat problem
Ángel Castro, Daniel Faraco, Francisco Mengual
We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixin…