Daniel Faraco

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20232026

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4 papers · 1 filter

math.AP2026

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 $Ω \subset R^{3}$ , we construct a divergence-free velocity field $u \in L_{t}^{1} W^{1, p} (Ω)$ for all $p < \infty$ , and magnetic fields $B^ε\in L_t^…

math.AP2025

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 $α$ -SQG equation with Sobolev regularity $W^{s, p}$ in the supercritical regime $s < α + \frac{2}{p}$ , covering the 2D Euler e…

math.AP2024

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 $L^{1} \cap L^{p}$ with $2 < p < \infty$ . The main simplification is an alt…

math.AP2023

Entropy solutions to macroscopic IPM

Ángel Castro, Daniel Faraco, Björn Gebhard

We investigate maximal potential energy dissipation as a selection criterion for subsolutions (coarse grained solutions) in the setting of the unstable Muskat problem. We show that…