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The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials
Younghun Hong, Stephen Pankavich
We study the relativistic and non-relativistic Vlasov equation driven by short-range interaction potentials and identify the large time dynamics of solutions. In particular, we con…
Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
Sonae Hadama, Younghun Hong
This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction…
Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
Sonae Hadama, Younghun Hong
The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form representing quantum states of infinitely many particles. In this articl…
Global existence versus finite time blowup dichotomy for the dispersion managed NLS
Mi-Ran Choi, Younghun Hong, Young-Ran Lee
We consider the Gabitov-Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity \[ i\partial_t u+ d_\text{av} \partial_x^2u+\int_0^1…