10 papers
Emergence of cuspons through wave breaking
Yunjoo Kim, Bongsuk Kwon
We study the emergence of cuspons through wave breaking, with the Camassa--Holm equation as a principal model. For a broad open class of smooth initial data, the first singularity…
Uniform Stability of degenerate Oleinik shock and rarefaction waves under large perturbations
Moon-Jin Kang, Bongsuk Kwon, Wanyong Shim
We study the uniform stability of composite waves consisting of a degenerate Oleinik shock and a rarefaction wave for scalar viscous conservation laws. We consider cubic-type fluxe…
Stable cusp formation for the Novikov equation
Yunjoo Kim, Dowan Koo, Bongsuk Kwon +1
We establish stable cusp formation for the Novikov equation, a cubically nonlinear Camassa--Holm-type equation. We identify an open set of smooth initial data for which the first g…
-contraction and asymptotic stability of Cahn-Hilliard fronts
Bongsuk Kwon, Wanyong Shim
We study the stability of transition fronts for the one-dimensional Cahn-Hilliard equation. More precisely, we prove that for any Hölder initial datum sufficiently close to a front…
Asymptotic self-similar blow-up for the regularized Saint-Venant equations
Yunjoo Kim, Bongsuk Kwon, Wanyong Shim
We investigate singularity formation in the regularized Saint--Venant (rSV) equations, a conservative, non-dispersive shallow water system that is formally regarded as a Hamiltonia…
Sharp regularity of gradient blow-up solutions in the Camassa-Holm equation
Yunjoo Kim, Bongsuk Kwon, Jeongsik Yoon
We study the formation of singularities in the Camassa-Holm (CH) equation, providing a detailed description of the blow-up dynamics and identifying the precise Hölder regularity of…
Long-Time Behavior towards Shock Profiles for the Navier-Stokes-Poisson System
Moon-Jin Kang, Bongsuk Kwon, Wanyong Shim
We study the stability of shock profiles in one spatial dimension for the isothermal Navier-Stokes-Poisson (NSP) system, which describes the dynamics of ions in a collision-dominat…
Singularity formation of hydromagnetic waves in cold plasma
Junsik Bae, Junho Choi, Bongsuk Kwon
We study blow-up of the compressible fluid model introduced by Gardner and Morikawa, which describes the dynamics of a magnetized cold plasma. We propose sufficient condition…
Delta-shock for the pressureless Euler-Poisson system
Junsik Bae, Yunjoo Kim, Bongsuk Kwon
We study singularity formation for the pressureless Euler-Poisson system of cold ion dynamics. In contrast to the Euler-Poisson system with pressure, when its smooth solutions expe…
Structure of singularities for the Euler-Poisson system of ion dynamics
Junsik Bae, Yunjoo Kim, Bongsuk Kwon
We study the formation of singularity for the isothermal Euler-Poisson system arising from plasma physics. Contrast to the previous studies yielding only limited information on the…