Ryan McConnell

collaborators

2 papers

math.AP2024

On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{- \frac{1}{2}} (T)$

Ryan McConnell, Seungly Oh

We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^{s} (T)$ for $s > - \frac{2}{3}$ . This wo…

math.AP2023

On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $T$

Ryan McConnell

We prove and utilize an improvement to the short time estimates of Burq, Gérard, & Tzvetkov on $T$ via connecting this estimate to the number of lattice points in thin ann…

On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below H−21​(T)

On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on T

On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{- \frac{1}{2}} (T)$

On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $T$