6 papers · 1 filter
No bubble trees for the -equivariant harmonic map heat flow and the radial energy-critical nonlinear heat equation in low dimensions
Taegyu Kim
We consider the -equivariant harmonic map heat flow (HMHF) from to and the radial energy-critical nonlinear heat equation (NLH) in dimensions $d=3,4,…
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…
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…
Quantized blow-up dynamics for Calogero--Moser derivative nonlinear Schrödinger equation
Uihyeon Jeong, Taegyu Kim
We consider the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS), an -critical nonlinear Schrödinger type equation enjoying a number of numerous structures,…
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…