2 citations · 2 across the 9 of their papers we have counts for
11 papers
Dynamics of the Drinfeld-Sokolov-Wilson system: well-posedness and (in)stability of the traveling waves
Ognyan Christov, Sevdzhan Hakkaev, Seungly Oh +1
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regulari…
On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below
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 for . This wo…
The Kato-Ponce Inequality with Polynomial Weights
Seungly Oh, Xinfeng Wu
We consider various versions of fractional Leibniz rules (also known as Kato-Ponce inequalities) with polynomial weights for . We sho…
Smoothing and growth bound of periodic generalized Korteweg-de Vries equation
Seungly Oh, Atanas G. Stefanov
For generalized KdV models with polynomial nonlinearity, we establish nonlinear smoothing property in for . Such smoothing effect persists globally, provided t…
Polynomial Bound and Nonlinear Smoothing for the Benjamin-Ono Equation on the Circle
Bradley Isom, Dionyssios Mantzavinos, Seungly Oh +1
For initial data in Sobolev spaces , , the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at…
Stabilization of Dispersion Generalized Benjamin Ono
Cynthia Flores, Seungly Oh, Derek Smith
In this article, we examine well-posedness and stabilization property of the dispersion-generalized Benjamin-Ono equation with periodic boundary conditions. The main ingredie…
The Kato-Ponce Inequality
Loukas Grafakos, Seungly Oh
In this article we develop a simplistic approach to revisit the classical Kato-Ponce inequality, which is also known as 'fractional Leibniz rule.' As a consequence, we derive the v…
Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries in low regularity settings
Seungly Oh
We show a smoothing effect of near full derivative for low-regularity global-in-time solutions of the periodic Korteweg-de Vries (KdV) equation. The smoothing is given by slightly…
Improved local well-posedness for the periodic "good" Boussinesq equation
Seungly Oh, Atanas Stefanov
We prove that the "good" Boussinesq model with the periodic boundary condition is locally well-posed in the space for . In the proof, we employ the…
On the periodic Korteweg-de Vries equation: a normal form approach
Seungly Oh
This paper discusses an improved smoothing phenomena for low-regularity solutions of the Korteweg-de Vries (KdV) equation in the periodic settings by means of normal form transform…
Local well-posedness for quadratic Schrödinger equations in : a normal form approach
Seungly Oh, Atanas Stefanov
For the Schrödinger equation $u_t+i u_{xx}=\nab^\be[u^2]$, $\be\in (0,1/2)$, we establish local well-posedness in $H^{\be-1+}$ (note that if $\be=0$, this matches, up to an endpoin…