Ahmed Dughayshim

collaborators

3 papers

math.AP2025

On well-posedness of the s-SchrÃ¶dinger maps in the subcritical regime

Ahmed Dughayshim

We study well-posedness of the $s$ -SchrÃ¶dinger map equation in dimension $n \geq 3$ in the subcritical regime, more precisely we establish a local well-posedness result when the i…

math.AP2025

Asymptotic Behaviour of fractional seminorms

Ahmed Dughayshim

We obtain asymptotically sharp identification of fractional Sobolev spaces $W_{p, q}^{s}$ , extension spaces $E_{p, q}^{s}$ , and Triebel-Lizorkin spaces $F ˙_{p, q}^{s}$ . In particu…

math.AP2025

Local well-posedness for cubic fractional SchrÃ¶dinger equations with derivatives on the right-hand side

Ahmed Dughayshim, Silvino Reyes Farina, Armin Schikorra

For $s \in (\frac{1}{2}, 1]$ we investigate well-posedness of the equation \[ \left ( i \partial_t + (-Î)^{s} \right ) u = \left (|D|^{1-2s} |u|^2 \right)\ |D|^{2s-1} u \] under sm…