66 citations · 398 across the 45 of their papers we have counts for
46 papers
Global dynamics above the ground state energy for the 3D Zakharov system
Zihua Guo, Kenji Nakanishi
We study the global dynamics for the 3D Zakharov system with radial initial data of energy slightly above the ground state energy, proving that the initial data set splits into nin…
Global dynamics around 2-solitons for the nonlinear damped Klein-Gordon equations
Kenjiro Ishizuka, Kenji Nakanishi
Global behavior of solutions is studied for the nonlinear Klein-Gordon equation with a focusing power nonlinearity and a damping term in the energy space on the Euclidean space. We…
Global wellposedness for the energy-critical Zakharov system below the ground state
Timothy Candy, Sebastian Herr, Kenji Nakanishi
The Cauchy problem for the Zakharov system in the energy-critical dimension is considered. We prove that global well-posedness holds in the full (non-radial) energy space for…
The Zakharov system in dimension
Timothy Candy, Sebastian Herr, Kenji Nakanishi
The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, pers…
Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
Jason Murphy, Kenji Nakanishi
We consider nonlinear Schrödinger equations with either power-type or Hartree nonlinearity in the presence of an external potential. We show that for long-range nonlinearities, sol…
Non-uniqueness for an energy-critical heat equation on
Slim Ibrahim, Hiroaki Kikuchi, Kenji Nakanishi +1
We construct a singular solution of a stationary nonlinear Schrödinger equation on with square-exponential nonlinearity having linear behavior around zero. In view o…