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math.AP2026
Scattering for the 4D Zakharov system below the ground state
Timothy Candy, Kenji Nakanishi
For the Zakharov system in four space dimensions, we prove that all solutions inside the potential well of the ground states are global and scattering in the energy space, with no…
math.AP2024
Global wellposedness of general nonlinear evolution equations for distributions on the Fourier half space
Kenji Nakanishi, Baoxiang Wang
The Cauchy problem is studied for very general systems of evolution equations, where the time derivative of solution is written by Fourier multipliers in space and analytic nonline…
math.AP2010
Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth
Lassaad Aloui, Slim Ibrahim, Kenji Nakanishi
We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a…