2 citations · 7 across the 19 of their papers we have counts for
21 papers
A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations
Shuji Machihara, Hayato Miyazaki, Tohru Ozawa
We present a unified framework for the rigorous derivation of conservation laws and related identities for nonlinear Schrödinger equations with power-type nonlinearities. This appr…
A comparison of the weakest contractive conditions for Banach and Kannan mappings
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous…
Exponential Decay of -Solutions to Stochastic Nonlinear Schrödinger Equations Driven by Continuous Martingales
Isamu Dôku, Shunya Hashimoto, Shuji Machihara
We investigate the global well-posedness and asymptotic behavior of -solutions to stochastic nonlinear Schrödinger equations with multiplicative noise driven by continuous squ…
Remarks on the derivation of the virial identity for nonlinear Schrödinger equations
Tomoyuki Ikeda, Shuji Machihara, Hayato Miyazaki +1
We revisit the derivation of the virial identity for nonlinear Schrödinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were de…
On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-c…
Global solution for the stochastic nonlinear Schrödinger system with quadratic interaction in four dimensions
Masaru Hamano, Shunya Hashimoto, Shuji Machihara
We discuss the global existence of solutions to a system of stochastic Schrödinger equations with multiplicative noise. Our setting of the quadratic nonlinear terms in dimension 4…
Global solutions of stochastic nonlinear Schrödinger system with quadratic interaction
Masaru Hamano, Shunya Hashimoto, Shuji Machihara
The time-global existence of solutions to a system of stochastic Schrödinger equations with multiplicative noise and the quadratic nonlinear terms are discussed in this paper. The…
Revisiting the Rellich inequality
Neal Bez, Shuji Machihara, Tohru Ozawa
We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial and spherical derivatives. This naturally leads to a comparison of the norms of the…
On the compactness of the (non)radial Sobolev spaces
Shuji Machihara, Megumi Sano
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an…
The well-posedness of the stochastic nonlinear Schrödinger equations in
Isamu Dôku, Shunya Hashimoto, Shuji Machihara
The Cauchy problem for the stochastic nonlinear Schrödinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients ar…
Blow-up solutions for non-scale-invariant nonlinear Schrödinger equation in one dimension
Masaru Hamano, Masahiro Ikeda, Shuji Machihara
In this paper, we consider the mass-critical nonlinear Schrödinger equation in one dimension. Ogawa--Tsutsumi [19] proved a blow-up result for negative energy solution by using a s…
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
Takahisa Inui, Shuji Machihara
We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay l…
Blowup solutions for the nonlinear Schrödinger equation with complex coefficient
Shota Kawakami, Shuji Machihara
We construct a finite time blow up solution for the nonlinear Schrödinger equation with the power nonlinearity whose coefficient is complex number. We generalize the range of both…
A supersolutions perspective on hypercontractivity
Yosuke Aoki, Jonathan Bennett, Neal Bez +3
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quan…
Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension
Shuji Machihara, Mamoru Okamoto
We show the ill-posedness of the Cauchy problem for the Dirac-Klein-Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the reg…
Remarks on the Rellich inequality
Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade
We study the Rellich inequalities in the framework of equalities. We present equalities which imply the Rellich inequalities by dropping remainders. This provides a simple and dire…
Remarks on the Hardy type inequalities with remainder terms in the framework of equalities
Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade
We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultane…
Global well-posedness for one dimensional Chern-Simons-Dirac system in
Shuji Machihara, Takayoshi Ogawa
Time global wellposedness in L^p for the Chern-Simons-Dirac equation in 1+1 dimension is discussed.
Extremisers for the trace theorem on the sphere
Neal Bez, Shuji Machihara, Mitsuru Sugimoto
We find all extremisers for the trace theorem on the sphere. We also provide a sharp extension for functions belonging to certain Sobolev spaces with angular regularity.
A note on the Chern-Simons-Dirac equations in the Coulomb Gauge
Nikolaos Bournaveas, Timothy Candy, Shuji Machihara
We prove that the Chern-Simons-Dirac equations in the Coulomb gauge are locally well-posed from initial data in H^s with s > 1/4 . To study nonlinear Wave or Dirac equations at thi…
Local and global well-posedness for the Chern-Simons-Dirac system in one dimension
Nikolaos Bournaveas, Timothy Candy, Shuji Machihara
We consider the Cauchy problem for the Chern-Simons-Dirac system on with initial data in . Almost optimal local well-posedness is obtained. Moreover, we sho…