14 citations · 107 across the 28 of their papers we have counts for
26 papers · 1 filter
Large-data modified wave operators for the defocusing nonlinear Schrödinger equation in one space dimension with subcritical long-range nonlinearity
Masaki Kawamoto, Haruya Mizutani
We study long-time behavior of the solutions to the final state problem for the defocusing nonlinear Schrödinger equation (NLS) in one space dimension with the power nonlinearity $…
Modified wave operators for the defocusing cubic nonlinear Schrödinger equation in one space dimension with large scattering data
Masaki Kawamoto, Haruya Mizutani
In the present paper, we construct modified wave operators for the defocusing cubic nonlinear Schrödinger equation (NLS) in one space dimension without size restriction on scatteri…
Modified scattering for the cubic nonlinear Schrödinger equation with long-range potentials in one space dimension
Masaki Kawamoto, Haruya Mizutani
We consider the cubic nonlinear Schrödinger equation with long-range linear potentials in one space dimension, and prove the modified scattering in the energy space for the associa…
Counterexamples and weak (1,1) estimates of wave operators for fourth-order Schrödinger operators in dimension three
Haruya Mizutani, Zijun Wan, Xiaohua Yao
This paper is dedicated to investigating the -bounds of wave operators associated with fourth-order Schrödinger operators on . We consid…
Modified scattering for nonlinear Schrödinger equations with long-range potentials
Masaki Kawamoto, Haruya Mizutani
We study the final state problem for the nonlinear Schrödinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic pro…
-boundedness of wave operators for bi-Schrödinger operators on the line
Haruya Mizutani, Zijun Wan, Xiaohua Yao
This paper is devoted to establishing several types of -boundedness of wave operators associated with the bi-Schrödinger operators on the…
Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki +2
We consider the final state problem for the inhomogeneous nonlinear Schrödinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a…
Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki +2
We consider the cubic nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initi…
Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials
Haruya Mizutani
We study the scattering theory for the Schrödinger and wave equations with rough potentials in a scale of homogeneous Sobolev spaces. The first half of the paper concerns with an i…
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with -data
Takahisa Inui, Haruya Mizutani
In the present paper, we consider the linear wave equation with the scale-invariant damping and mass. It is known that the global behavior of the solution depends on the size of th…
Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass
Takahisa Inui, Haruya Mizutani
We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our a…
Global Kato smoothing and Strichartz estimates for higher-order Schrödinger operators with rough decay potentials
Haruya Mizutani, Xiaohua Yao
Let \( H = (-Δ)^m + V \) be a higher-order elliptic operator on \( L^2(\mathbb{R}^n) \), where \( V \) is a general bounded decaying potential. This paper focuses on the global Kat…
Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials
Haruya Mizutani, Xiaohua Yao
Let and be Schrödinger type operators on with a class of scaling-critical potentials , which include the Hardy potential …
Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph
Kazuki Aoki, Takahisa Inui, Haruya Mizutani
We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, , o…
Uniform resolvent estimates for Schrödinger operator with an inverse-square potential
Haruya Mizutani, Junyong Zhang, Jiqiang Zheng
We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let where is the usual Laplacian on $\mathbb{R}^…
Wave operators on Sobolev spaces
Haruya Mizutani
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from…
Strichartz estimates for Schrödinger equations with slowly decaying potentials
Haruya Mizutani
For Schrödinger equations with a class of slowly decaying repulsive potentials, we show that the solution satisfies global-in-time Strichartz estimates for any admissible pairs. Ou…
Global-in-time smoothing effects for Schrödinger equations with inverse-square potentials
Haruya Mizutani
The purpose of this note is to prove global-in-time smoothing effects for the Schrödinger equation with potentials exhibiting critical singularity. A typical example of admissible…
Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications
Haruya Mizutani
We prove uniform Sobolev estimates for the resolvent of Schrödinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-tim…
Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities
Jean-Marc Bouclet, Haruya Mizutani
This paper deals with global dispersive properties of Schrödinger equations with real-valued potentials exhibiting critical singularities, where our class of potentials is more gen…
Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
Haruya Mizutani
The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the Schrödinger equation on , , with the negative inverse-square…
Global in time Strichartz inequalities on asymptotically flat manifolds with temperate trapping
Jean-Marc Bouclet, Haruya Mizutani
We prove global Strichartz inequalities for the Schrödinger equation on a large class of asymptotically conical manifolds. Letting be the nonnegative Laplace operator and $ f…
Strichartz estimates for non elliptic Schrödinger equations on compact manifolds
Haruya Mizutani, Nikolay Tzvetkov
In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate…
Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials II. Superquadratic potentials
Haruya Mizutani
In this paper we prove local-in-time Strichartz estimates with loss of derivatives for Schrödinger equations with variable coefficients and potentials, under the conditions that th…