Florida International University

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19922026

most citedThe Gaia mission

7.1k citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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49 papers · 1 filter

math.AP2026

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Iryna Petrenko, Oscar Riaño, Svetlana Roudenko

In this paper we consider the 4th order (or biharmonic) nonlinear Schrödinger (NLS) equation in dimensions 1, 2, and 3, where the potential term is expressed as a power non-lineari…

math.AP2026

Spectral property for the 2D Zakharov-Kuznetsov equation

Justin Holmer, Svetlana Roudenko

We discuss a spectral property for the virial operator of the 2D Zakharov-Kuznetsov (ZK) equation. This is a crucial ingredient to establish blow-up or asymptotic stability of soli…

math.AP2026

The nonlinear Schrödinger equation with combined nonlinearities in 1D

Oscar Riaño, Alex D Rodriguez, Svetlana Roudenko

We consider the one-dimensional nonlinear Schrödinger equation $i u_{t} + u_{xx} + N (u) u = 0, x, t \in R,$ with the nonlinearity term that is expressed as a s…

math.AP2025★ 3 cited

Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation

Christian Klein, Iryna Petrenko, Svetlana Roudenko +1

We consider the one dimensional 4th order, or bi-harmonic, nonlinear Schrödinger (NLS) equation, namely, $i u_{t} - Δ^{2} u - 2 a Δ u + ∣ u ∣^{α} u = 0, x, a \in R$ , $α > 0$ , and investigate…

math.AP2025

Strong and weak solutions to a structural acoustic model with a $C^{1}$ source term on the plate

Andrew R. Becklin, Yanqiu Guo

In this manuscript, we consider a structural acoustic model consisting of a wave equation defined in a bounded domain $Ω \subset R^{3}$ , strongly coupled with a Berger plate…

math.AP2024

Optimal Boundary Control for the Stochastic Allen-Cahn Navier-Stokes system in two dimensions

R. D. Ayissi, G. Deugoue, J. Ngandjou Zangue +1

In this work, we study an optimal boundary control for the stochastic Allen Cahn Navier Stokes system. The governing system of nonlinear partial differential equations consists of…

math.AP2022★ 8 cited

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Isaac Friedman, Oscar Riaño, Svetlana Roudenko +2

We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers…

math.AP2021★ 3 cited

A Generalized CR equation with isolated singularities

B. de Lessa Victor, Adbelhamid Meziani

The generalized CR equation $u_{z ˉ} = a u + b u ˉ + f$ is studied when the coefficients $a$ and $b$ have a finite number of singular points inside the domain. Solutions are constr…

math.AP2021

Regularity and stability of the semigroup associated with some interacting elastic systems I: A degenerate damping case

K. Ammari, F. Shel, L. Tebou

In this paper, we examine regularity and stability issues for two damped abstract elastic systems. The damping involves the average velocity and a fractional power $θ$ , with $θ$ in…

math.AP2020★ 9 cited

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

C. Klein, S. Roudenko, N. Stoilov

We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Kortewe…

math.AP2020★ 14 cited

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

Svetlana Roudenko, Zhongming Wang, Kai Yang

We consider the generalized Benjamin-Ono (gBO) equation on the real line, $u_{t} + \partial_{x} (- H u_{x} + \frac{1}{m} u^{m}) = 0, x \in R, m = 2, 3, 4, 5$ , and perform nu…

math.AP2020★ 9 cited

On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation

Oscar Riaño

Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights…

math.AP2020★ 10 cited

Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle

Thomas Duyckaerts, Oussama Landoulsi, Svetlana Roudenko

We study the dynamics of the focusing $3 d$ cubic nonlinear Schrödinger equation in the exterior of a strictly convex obstacle at the mass-energy threshold, namely, when $ E_Ω[u_0]…

math.AP2020★ 2 cited

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Annie Millet, Alex D Rodriguez, Svetlana Roudenko +1

We study the focusing stochastic nonlinear Schrödinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, i…

math.AP2020★ 11 cited

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Annie Millet, Svetlana Roudenko, Kai Yang

We study the focusing stochastic nonlinear Schrödinger equation in 1D in the $L^{2}$ -critical and supercritical cases with an additive or multiplicative perturbation driven by space-…

math.AP2020★ 21 cited

Numerical study of Zakharov-Kuznetsov equations in two dimensions

C. Klein, S. Roudenko, N. Stoilov

We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the $L^{2}$ -subc…

math.AP2019

Regularity of solutions of quasi-linear elliptic equations with $L lo g^{m} L$ coefficients

Julian Edward, Steve Hudson, Mark Leckband

Let $D$ be an bounded region in $R^{n}$ . The regularity of solutions of a family of quasilinear elliptic partial differential equations is studied, one example being $Δ_nu=Vu^{…

math.AP2019

Thinking Inside the Box: An Advection-Diffusion Model of Animal Movement in an Enclosed Region

Stephen Tennenbaum, John Gatto, Joel Trexler

We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time mov…

math.AP2019★ 18 cited

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Debdeep Bhattacharya, Luiz Gustavo Farah, Svetlana Roudenko

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$ -method, we prove the global well-posedness o…

math.AP2019★ 59 cited

Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation

Luccas Campos

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schrödinger equation \begin{equation} iu_t + Δu + |x|^{-b}|u|^{p-1}u=0, \end{equation}…

math.AP2019★ 8 cited

On the Well-posedness of Reduced $3 D$ Primitive Geostrophic Adjustment Model with Weak Dissipation

Chongsheng Cao, Quyuan Lin, Edriss S. Titi

In this paper we prove the local well-posedness and global well-posedness with small initial data of the strong solution to the reduced $3 D$ primitive geostrophic adjustment model…

math.AP2019

Class of hypocomplex structures on the two dimensional torus

Abdelhamid Meziani, Giuliano Zugliani

We study the Hölder solvability of a class of complex vector fields on the torus $T^{2}$ . We make use of the Theta function to associate a Cauchy-Pompeiu type integral opera…

math.AP2018★ 18 cited

Blow-up dynamics in the mass super-critical NLS equations

Kai Yang, Svetlana Roudenko, Yanxiang Zhao

We study stable blow-up dynamics in the $L^{2}$ -supercritical nonlinear Schrödinger equation in various dimensions. We first investigate the profile equation and extend the result of…

math.AP2018★ 1 cited

Well-posedness results for a class of semi-linear super-diffusive equations

Edgardo Alvarez, Ciprian Gal, Valentin Keyantuo +1

In this paper we investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{α}u(t)+Au(t)=f(u(t)), & 1<α<2, u(0)=u_{0},\,\,\,u…

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Spectral property for the 2D Zakharov-Kuznetsov equation

The nonlinear Schrödinger equation with combined nonlinearities in 1D

Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation

Strong and weak solutions to a structural acoustic model with a C1 source term on the plate

Optimal Boundary Control for the Stochastic Allen-Cahn Navier-Stokes system in two dimensions

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

A Generalized CR equation with isolated singularities

Regularity and stability of the semigroup associated with some interacting elastic systems I: A degenerate damping case

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation

Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Behavior of solutions to the 1D focusing stochastic L2-critical and supercritical nonlinear Schrödinger equation with space-time white noise

Numerical study of Zakharov-Kuznetsov equations in two dimensions

Regularity of solutions of quasi-linear elliptic equations with LlogmL coefficients

Thinking Inside the Box: An Advection-Diffusion Model of Animal Movement in an Enclosed Region

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation

On the Well-posedness of Reduced 3D Primitive Geostrophic Adjustment Model with Weak Dissipation

Class of hypocomplex structures on the two dimensional torus

Blow-up dynamics in the mass super-critical NLS equations

Well-posedness results for a class of semi-linear super-diffusive equations

Strong and weak solutions to a structural acoustic model with a $C^{1}$ source term on the plate

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Regularity of solutions of quasi-linear elliptic equations with $L lo g^{m} L$ coefficients

On the Well-posedness of Reduced $3 D$ Primitive Geostrophic Adjustment Model with Weak Dissipation