Francisco Mengual

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

math.AP2026

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 $H ˙^{s}$ - energy solutions below the Miura-Ju class. In particular, t…

math.AP2025

Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation

Ãngel Castro, Daniel Faraco, Francisco Mengual +1

We prove non-uniqueness of weak solutions to the forced $I^\pm$ -SQG equation with Sobolev regularity $W^{s, p}$ in the supercritical regime $s < I^\pm + \frac{2}{p}$ , covering the 2D Euler…

math.AP2024

A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation

Ãngel 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…