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A log-log upper bound on blow-up rates for the mass-critical half-wave equation
Taegyu Kim, Soonsik Kwon, Jeongheon Park
We study finite-time blow-up for the one-dimensional focusing mass-critical half-wave equation \begin{equation*} i\partial_tu=|D|u-|u|^2u. \end{equation*} For even initial data wit…
A universal bound on the blow-up rate for the focusing mass-critical nonlinear Schrödinger equation
Beomjong Kwak, Soonsik Kwon
In this paper, we investigate a universal blow-up bound for the focusing mass-critical nonlinear Schrödinger equation for general initial data in , extending prev…
Classification of single-bubble blow-up solutions for Calogero--Moser derivative nonlinear Schrödinger equation
Uihyeon Jeong, Kihyun Kim, Taegyu Kim +1
We study the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS), a mass-critical and completely integrable dispersive model. Recent works established finite-time b…
Blow-up construction and instability for mass-critical half-wave equation with slightly superthreshold mass
Taegyu Kim, Soonsik Kwon, Jeongheon Park
We study the blow-up dynamics for the -critical focusing half-wave equation on the real line, a nonlocal dispersive PDE arising in various physical models. As in other mass-cr…
Critical local well-posedness of the nonlinear Schrödinger equation on the torus
Beomjong Kwak, Soonsik Kwon
In this paper, we study the local well-posedness of nonlinear Schrödinger equations on tori at the critical regularity. We focus on cases where the nonlinearity $|…
Blow-up dynamics for radial self-dual Chern-Simons-Schrödinger equation with prescribed asymptotic profile
Kihyun Kim, Soonsik Kwon, Sung-Jin Oh
We construct finite energy blow-up solutions for the radial self-dual Chern-Simons-Schrödinger equation with a continuum of blow-up rates. Our result stands in stark contrast to th…
Soliton resolution for Calogero--Moser derivative nonlinear Schrödinger equation
Taegyu Kim, Soonsik Kwon
We consider soliton resolution for the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by Gérard an…