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20 papers · 1 filter
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…
Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth
Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee
We prove the Wolff potential estimates for nonlocal equations with Orlicz growth. As an application, we obtain the Wiener criterion in this framework, which provides a necessary an…
The fractional -Laplacian on hyperbolic spaces
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We present three equivalent definitions of the fractional -Laplacian , , , with normalizing constants, on hyperbolic spaces. The expli…
Well-posedness of a nonlinear shallow water model for an oscillating water column with time-dependent air pressure
Edoardo Bocchi, Jiao He, Gastón Vergara-Hermosilla
We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device is refo…
A paradifferential approach for hyperbolic dynamical systems and applications
Yannick Guedes Bonthonneau, Colin Guillarmou, Thibault de Poyferré
We develop a paradifferential approach for studying non-smooth hyperbolic dynamics and related non-linear PDE from a microlocal point of view. As an application, we describe the mi…
The Regularity Theory for the Double Obstacle Problem for Fully Nonlinear Operator
Ki-ahm Lee, Jinwan Park
In this paper, we prove the existence and uniqueness of () solutions of a double obstacle problem with obstacle functions. Moreover, we show the opt…