12 citations · 61 across the 24 of their papers we have counts for
24 papers
Global well-posedness for intermediate NLS with nonvanishing conditions at infinity
Takafumi Akahori, Rana Badreddine, Slim Ibrahim +1
The intermediate nonlinear Schrödinger equation (INLS) describes the dynamics of the envelope of weakly nonlinear internal waves in a stratified fluid of finite depth. While the IN…
Unconditional uniqueness for the derivative nonlinear Schrödinger equation by normal form approach
Nobu Kishimoto
We prove uniqueness of solutions to the Cauchy problem for the derivative nonlinear Schrödinger equation in . Our proof is based on the method of normal form r…
Global solution and asymptotic behavior for the kinetic derivative NLS on
Nobu Kishimoto, Kiyeon Lee
In this paper we investigate the global well-posedness and long-term behavior of solutions to the kinetic derivative nonlinear Schrödinger equation (KDNLS) on the real line. The eq…
Local and global well-posedness for the kinetic derivative NLS on
Nobu Kishimoto, Kiyeon Lee
We investigate the local and global well-posedness of the kinetic derivative nonlinear Schrödinger equation (KDNLS) on , described by \[ i\partial_t u + \partial_x^2 u…
Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method
Nobu Kishimoto, Yoshio Tsutsumi
In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlin…
Gauge transformation for the kinetic derivative nonlinear Schrödinger equation on the torus
Nobu Kishimoto, Yoshio Tsutsumi
We consider the kinetic derivative nonlinear Schrödinger equation, which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the H…
Characterization of three-dimensional Euler flows supported on finitely many Fourier modes
Nobu Kishimoto, Tsuyoshi Yoneda
Recently, the Nash-style convex integration has been becoming the main scheme for the mathematical study of turbulence, and the main building block of it has been either Beltrami f…
Well-posedness of the Cauchy Problem for the Kinetic DNLS on
Nobu Kishimoto, Yoshio Tsutsumi
We consider the Cauchy problem for the kinetic derivative nonlinear Schrödinger equation on the torus: \[ \partial_t u - i \partial_x^2 u = α\partial_x \big( |u|^2 u \big) + β\part…
Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations
Andreia Chapouto, Nobu Kishimoto
In this paper, we study the Gibbs measures for periodic generalized Korteweg-de Vries equations (gKdV) with quartic or higher nonlinearities. In order to bypass the analytical ill-…
Unconditional local well-posedness for periodic NLS
Nobu Kishimoto
The nonlinear Schrödinger equations with nonlinearities on the -dimensional torus are considered for arbitrary positive integers and . The solution of the Cau…
Unconditional uniqueness for the periodic modified Benjamin-Ono equation by normal form approach
Nobu Kishimoto
We show that the solution (in the sense of distribution) to the Cauchy problem with the periodic boundary condition associated with the modified Benjamin-Ono equation is unique in…
Unconditional uniqueness for the periodic Benjamin-Ono equation by normal form approach
Nobu Kishimoto
We show unconditional uniqueness of solutions to the Cauchy problem associated with the Benjamin-Ono equation under the periodic boundary condition with initial data given in …
Unconditional uniqueness of solutions for nonlinear dispersive equations
Nobu Kishimoto
When a solution to the Cauchy problem for nonlinear dispersive equations is obtained by a fixed point argument using auxiliary function spaces, it is non-trivial to ensure uniquene…
Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition
Takahisa Inui, Nobu Kishimoto, Kuranosuke Nishimura
We consider a mass-critical system of nonlinear Schödinger equations \begin{align*} \begin{cases} i\partial_t u +Δu =\bar{u}v,\\ i\partial_t v +κΔv =u^2, \end{cases} (t,x)\in \math…
Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance
Takahisa Inui, Nobu Kishimoto, Kuranosuke Nishimura
We consider the quadratic nonlinear Schrödinger system \begin{align*} \begin{cases} i\partial_t u +Δu =v \overline{u},\\ i\partial_t v +κΔv =u^2, \end{cases} \text{ on } I \times \…
A remark on norm inflation for nonlinear Schrödinger equations
Nobu Kishimoto
We consider semilinear Schrödinger equations with nonlinearity that is a polynomial in the unknown function and its complex conjugate, on or on the torus. Norm infla…
Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term
Nobu Kishimoto, Yoshio Tsutsumi
We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a…
Global solvability of the rotating Navier-Stokes equations with fractional Laplacian in a periodic domain
Nobu Kishimoto, Tsuyoshi Yoneda
We consider existence of global solutions to equations for three-dimensional rotating fluids in a periodic frame provided by a sufficiently large Coriolis force. The Coriolis force…
A number theoretical observation of a resonant interaction of Rossby waves
Nobu Kishimoto, Tsuyoshi Yoneda
Rossby waves are generally expected to dominate the plane dynamics in geophysics, and here in this paper we give a number theoretical observation of the resonant interaction wi…
Resonant decomposition and the -method for the two-dimensional Zakharov system
Nobu Kishimoto
The initial value problem of the Zakharov system on two-dimensional torus with general period is considered in this paper. We apply the -method with some 'resonant decomposition…
Sharp local well-posedness for the "good" Boussinesq equation
Nobu Kishimoto
In the present article, we prove the sharp local well-posedness and ill-posedness results for the "good" Boussinesq equation on ; the initial value problem is locally w…
Remark on the periodic mass critical nonlinear Schrödinger equation
Nobu Kishimoto
We consider the mass critical NLS on and . In the case the Strichartz estimates enable us to show well-posedness of the IVP in (at l…
Local well-posedness for the Zakharov system on multidimensional torus
Nobu Kishimoto
The initial value problem of the Zakharov system on two dimensional torus with general period is shown to be locally well-posed in the Sobolev spaces of optimal regularity, includi…
Construction of blow-up solutions for Zakharov system on
Nobu Kishimoto, Masaya Maeda
We consider the Zakharov system in two space dimension with periodic boundary condition. We prove the existence of finite time blow-up solutions. Further, we show there exists no m…