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Silvino Reyes Farina

Publications and source records attributed to Silvino Reyes Farina.

4 recordsLinked to original sources
arXiv2025

On uniqueness for hyperbolic half-wave maps in dimension $d \geq 3$

Half-wave maps appear in the physics literature as the continuum limit of Calogero-Moser spin systems. We obtain a uniqueness result for the Half-Wave Maps equation in dimension $d \ge 3$ in the natural energy class with $\mathbb{H}^2$ target. In the proof, we differentiate in time to arrive at a wave-type equation and isometrically embed $\mathbb{H}^2$ into some $\mathbb{R}^m$ using the Nash embedding theorem. Relying on geometric properties of $\mathbb{H}^2$, combined with fractional Leibniz rules and commutator estimates, we then use a Grönwall inequality argument to obtain uniqueness.

math.AP↗
arXiv2025

Local well-posedness for cubic fractional Schrödinger equations with derivatives on the right-hand side

For $s \in (\frac{1}{2},1]$ we investigate well-posedness of the equation \[ \left ( i \partial_t + (-Δ)^{s} \right ) u = \left (|D|^{1-2s} |u|^2 \right)\ |D|^{2s-1} u \] under small initial data $\|u(0)\|_{H^{\frac{n-2s}{2}}(\mathbb{R}^n)} \ll 1$. This equation is a model equation for for $s$-Schrödinger map equation \[ \partial_t ψ= ψ\wedge (-Δ)^s ψ: \quad ψ: \mathbb{R}^n \times \mathbb{R} \to \mathbb{S}^{2}, \]

math.AP↗
arXiv2024

On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps

We prove a priori estimates for wave systems of the type \[ \partial_{tt} u - Δu = Ω\cdot du + F(u) \quad \text{in $\mathbb{R}^d \times \mathbb{R}$} \] where $d \geq 4$ and $Ω$ is a suitable antisymmetric potential. We show that the assumptions on $Ω$ are applicable to wave- and half-wave maps, the latter by means of the Krieger-Sire reduction. We thus obtain well-posedness of those equations for small initial data in $\dot{H}^{\frac{d}{2}}(\mathbb{R}^d)$.

math.AP↗