17 citations · 83 across the 17 of their papers we have counts for
17 papers
Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma i…
A note on Strichartz estimates for the wave equation with orthonormal initial data
Neal Bez, Shinya Kinoshita, Shobu Shiraki
This note is concerned with Strichartz estimates for the wave equation and orthonormal families of initial data. We provide a survey of the known results and present what seems to…
Boundary Strichartz estimates and pointwise convergence for orthonormal systems
Neal Bez, Shinya Kinoshita, Shobu Shiraki
We consider maximal estimates associated with fermionic systems. First we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cas…
Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system
Shinya Kinoshita, Shohei Nakamura, Akansha Sanwal
In this paper, we establish local well-posedness for the Zakharov system on , in a low regularity setting. Our result improves the work of Kishimoto. Moreover…
Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schrödinger equation with angular regularity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schrödinger equation in with the nonlinearity where $η\in \math…
Local well-posedness of a system describing laser-plasma interactions
Sebastian Herr, Isao Kato, Shinya Kinoshita +1
A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is a coupled system of a Schrödinger and a wave equation with a non-dispersive d…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations introduced by Colin and Colin (2004). We determine an almost opt…
The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity
Sebastian Herr, Shinya Kinoshita
The Zakharov-Kuznetsov equation in spatial dimension is considered. The Cauchy problem is shown to be globally well-posed for small initial data in critical spaces and it…
Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation
Shinya Kinoshita, Robert Schippa
Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in the fully periodic case with initial data in Sobolev spaces , , is proved. Frequency dependent…
Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
Sebastian Herr, Shinya Kinoshita
The Zakharov-Kuznetsov equation in space dimension is considered. It is proved that the Cauchy problem is locally well-posed in in the full subcritica…
Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation
Shinya Kinoshita
This paper is concerned with the Cauchy problem of the modified Zakharov-Kuznetsov equation on . If , we prove the sharp estimate which implies local in time wel…
Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
Shinya Kinoshita
This paper is concerned with the Cauchy problem of the D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space $…
Well-posedness for KdV-type equations with quadratic nonlinearity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of the KdV-type equation \[ \partial_t u + \frac{1}{3} \partial_x^3 u = c_1 u \partial_x^2u + c_2 (\partial_x u)^2, \quad u(0)=u_0. \] Pilod (2008) s…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (200…
Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations for the spatial dimension and . This system was…
Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions
Isao Kato, Shinya Kinoshita
We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension with initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0} \in H^{s+1}(\mathbb{R}^…
Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D
Shinya Kinoshita
This paper is concerned with the Cauchy problem of D Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get…