22 citations · 30 across the 11 of their papers we have counts for
16 papers
On the parabolic model for the harmonic oscillator II: global existence and invariant measures
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We establish an a priori bound for the dynamical parabolic model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bo…
An Effective SPDE Model for a Schrödinger Equation with a Fluctuating Magnetic Potential
Franco Flandoli, Reika Fukuizumi, Francesco Grotto +1
We consider the Schrödinger equation for a charged particle in a randomly fluctuating external magnetic field and establish a singular perturbation limit in which the solution conv…
Ergodicity for a Constantin-Lax-Majda-DeGregorio model of turbulent flow
Shunsuke Fujita, Reika Fukuizumi, Takashi Sakajo
This paper presents a mathematical analysis of a one-dimensional model of turbulence based on a stochastic generalized Constantin-Lax-Majda-DeGregorio (gCLMG) equation. We focus on…
Besov spaces associated with the Harmonic oscillator
Reika Fukuizumi, Tsukasa Iwabuchi
The Besov space associated with the harmonic oscillator is introduced and thoroughly explored in this paper. It provides a comprehensive summary of the fundamental concepts of the…
On the parabolic model for the harmonic oscillator: diagrams and local existence
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We prove the local wellposedness of the (renormalized) parabolic model associated with the harmonic oscillator on , that is, the equation formally written as…
The stochastic fast logarithmic equation in with multiplicative Stratonovich noise
Ioana Ciotir, Reika Fukuizumi, Dan Goreac
This paper is concerned with the existence and uniqueness of the solution for the stochastic fast logarithmic equation with Stratonovich multiplicative noise in fo…
Renormalization of a 1d quadratic Schr{ö}dinger model with additive noise
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
The study is devoted to the interpretation and wellposedness of the stochastic NLS model \begin{equation*} (\imath \partial_t-Δ)u=|u|^2+\dot{B}, \quad u_0=0,\quad \quad t\in \mathb…
Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation
Reika Fukuizumi, Yueyuan Gao, Guido Schneider +1
In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-…
Stationary martingale solution for the 2D stochastic Gross-Pitaevskii equation
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
In this short report we give a proof of the existence of a stationary solution to the Gross-Pitaevskii equation in driven by a space-time white noise.
Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation
Reika Fukuizumi, Masato Hoshino, Takahisa Inui
We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time white noise on the torus. In order…
Two dimensional Gross-Pitaevskii equation with space-time white noise
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is…
Stochastic Schrödinger-Lohe model
Reika Fukuizumi, Leo Hahn
The Schrödinger-Lohe model consists of wave functions interacting with each other, according to a system of Schrödinger equations with a specific coupling such that all wave functi…
Scattering for the supercritical point NLS
Riccardo Adami, Reika Fukuizumi, Justin Holmer
We consider the 1D nonlinear Schrödinger equation with focusing point nonlinearity. "Point" means that the pure-power nonlinearity has an inhomogeneous potential and the potential…
Long time behavior of Gross-Pitaevskii equation at positive temperature
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with…
Derivation of the Bose-Hubbard model in the multiscale limit
Reika Fukuizumi, Andrea Sacchetti
In this paper we consider a one-dimensional non-linear Schroedinger equation (NLSE) with a periodic potential. In the semiclassical limit we prove that the stationary solutions of…
Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit
Reika Fukuizumi, Andrea Sacchetti
We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we…