Benjamin Dodson

Global well-posedness of the energy subcritical nonlinear wave equation with initial data in a critical space

Benjamin Dodson

In this paper we prove global well-posedness for the defocusing, energy-subcritical, nonlinear wave equation on $R^{1 + 3}$ with initial data in a critical Besov space. No…

Global well-posedness and scattering for the radial, defocusing, cubic nonlinear wave equation

Benjamin Dodson

In this paper we prove global well-posedness and scattering for the defocusing, cubic, nonlinear wave equation on $R^{1 + 3}$ with radial initial data lying in the critica…

Global well-posedness and scattering for the defocusing, $L^{2}$ -critical, nonlinear Schr{Ã¶}dinger equation when $d \geq 3$

Benjamin Dodson

In this paper we prove that the defocusing, $d$ -dimensional mass critical nonlinear Schr{Ã¶}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(…

math.AP2014

Global well - posedness and scattering for the focusing, energy - critical nonlinear SchrÃ¶dinger problem in dimension $d = 4$ for initial data below a ground state threshold

Benjamin Dodson

In this paper we prove global well - posedness and scattering for the focusing, energy - critical nonlinear SchrÃ¶dinger initial value problem in four dimensions. Previous work pro…

Sequential convergence of a solution to the Chern--Simons--Schrodinger equation

Benjamin Dodson

In this paper we prove a sequential convergence result for blowup solutions to the $m$ -equivariant, self-dual Chern--Simons--Schr{Ã¶}dinger equation. We show that if $u$ has mass l…

Sharp Global well-posedness and scattering for the radial nonlinear intercritical wave equation

Benjamin Dodson

In this paper we prove global well-posedness and scattering for the defocusing, intercritical nonlinear wave equation in dimensions $d \geq 4$ with radial initial data. We prove th…

The $L^{2}$ sequential convergence of a solution to the one dimensional, mass-critical NLS above the ground state

Benjamin Dodson

In this paper we generalize a weak sequential result of \cite{fan20182} to any non-scattering solutions in one dimension. No symmetry assumptions are required for the initial data.

Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial data

Benjamin Dodson

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in a slightly supercritical Sobolev space, and a weighted…

math.AP2013

A controlling norm for energy-critical SchrÃ¶dinger maps

Benjamin Dodson, Paul Smith

We consider energy-critical Schroedinger maps with target either the sphere S^2 or hyperbolic plane H^2 and establish that a unique solution may be continued so long as a certain s…

The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures

Benjamin Dodson, Avraham Soffer, Thomas Spencer

We study the nonlinear SchrÃ¶dinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. O…

Instability of the soliton for the focusing, mass-critical generalized KdV equation

Benjamin Dodson, Cristian Gavrus

In this paper we prove instability of the soliton for the focusing, mass-critical generalized KdV equation. We prove that the solution to the generalized KdV equation for any initi…

Global well-posedness and scattering for the mass critical nonlinear Schr{Ã¶}dinger equation with mass below the mass of the ground state

Benjamin Dodson

In this paper we prove that the focusing, $d$ -dimensional mass critical nonlinear Schr{Ã¶}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\m…

math.AP2014

Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm

Benjamin Dodson, Andrew Lawrie

In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the mode…

math.AP2012

Bilinear Strichartz estimates for the Schr{Ã¶}dinger map problem

Benjamin Dodson

In this paper we prove bilinear Strichartz estimates for a solution to the Schr{Ã¶}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}…

Scattering for the defocusing, cubic nonlinear Schr{Ã¶}dinger equation with initial data in a critical space

Benjamin Dodson

In this note we prove scattering for a defocusing nonlinear Schr{Ã¶}dinger equation with initial data lying in a critical Besov space. In addition, we obtain polynomial bounds on t…

Spacetime integral bounds for the energy-critical nonlinear wave equation

Benjamin Dodson

In this paper we prove a global spacetime bound for the quintic, nonlinear wave equation in three dimensions. This bound depends on the $L_{t}^{\infty} L_{x}^{2}$ and $L_{t}^{\inft…

math.AP2026

Global well--posedness for the mass--critical nonlinear Schr{Ã¶}dinger equation on $T$

Benjamin Dodson

We prove a global well--posedness result for the quintic NLS on $T$ for initial data in $H^{s} (T)$ , $s > 1/3$ . This improves the previous best bound of $s > 2/5$ .

math.AP2026

Quantitative Scattering for the Energy-Critical Wave Equation on Asymptotically Flat Spacetimes

Benjamin Dodson, Sam Looi

We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations…

math.AP2016

A new proof of scattering below the ground state for the 3d radial focusing cubic NLS

Benjamin Dodson, Jason Murphy

We revisit the scattering result of Holmer and Roudenko on the radial focusing cubic NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz estimat…

A Liouville theorem for the Chern--Simons--Schr{Ã¶}dinger equation

Benjamin Dodson

In this paper we prove a Liouville theorem for the Chern--Simons--Schr{Ã¶}dinger equation. This result is consistent with the soliton resolution conjecture for initial data that do…

math.AP2009

Almost Morawetz estimates and global well-posedness for the defocusing $L^{2}$ -critical nonlinear Schr{Ã¶}dinger equation in higher dimensions

Benjamin Dodson

In this paper, we consider the global well-posedness of the defocusing, $L^{2}$ - critical nonlinear Schr{Ã¶}dinger equation in dimensions $n \geq 3$ . Using the I-method, we show t…

math.AP2025

Schr{Ã¶}dinger maps to a K{Ã¤}hler manifold in two dimensions

Benjamin Dodson, Jeremy L. Marzuola

We prove a global well--posedness and scattering result for Schr{Ã¶}dinger maps to a general K{Ã¤}hler manifold with small initial data in a Besov space.

math.AP2016

Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

Benjamin Dodson

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1, 1}^{2} \times B_{1, 1}^{1}$ . This space of functio…

math.AP2009

Global well-posedness for the defocusing, quintic nonlinear SchrÃ¶dinger equation in one dimension

Benjamin Dodson

In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear SchrÃ¶dinger equation. We show that a unique solution exi…

math.AP2019

Scattering below the ground state for the 2 $d$ radial nonlinear SchrÃ¶dinger equation

Anudeep Kumar Arora, Benjamin Dodson, Jason Murphy

We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear SchrÃ¶dinger equation in two space dimensions. We present a simp…

math.AP2014

Scattering for the radial 3d cubic wave equation

Benjamin Dodson, Andrew Lawrie

Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \ti…

math.AP2013

Global well-posedness and scattering for the defocusing, mass - critical generalized KdV equation

Benjamin Dodson

In this paper we prove that the defocusing, mass - critical generalized KdV initial value problem is globally well-posed and scattering for $u_{0} \in L^{2} (R)$ . We prove…

The $L^{2}$ sequential convergence of a solution to the mass-critical NLS above the ground state

Benjamin Dodson

In this paper we generalize a weak sequential result of \cite{fan20182} to a non-scattering solutions in dimension $d \geq 2$ . No symmetry assumptions are required for the initial…

The profile decomposition for the hyperbolic SchrÃ¶dinger equation

Benjamin Dodson, Jeremy L. Marzuola, Benoit Pausader +1

In this note, we prove the profile decomposition for hyperbolic SchrÃ¶dinger (or mixed signature) equations on $R^{2}$ in two cases, one mass-supercritical and one mass-crit…

Global well - posedness for the defocusing, cubic, nonlinear wave equation in three dimensions for radial initial in $H ˙^{s} \times H ˙^{s - 1}$ , $s > \frac{1}{2}$

Benjamin Dodson

In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $H ˙^{1/2} \times H ˙^{- 1/2}$ . We s…

Global well-posedness for the defocusing, cubic, nonlinear Schrodinger equation when n = 3 via a linear-nonlinear decomposition

Benjamin Dodson

In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schr{Ã¶}dinger equation in three dimensions when $n = 3$ when $u_{0} \in H^{s}(\mat…

On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System

Benjamin Dodson, Nishanth Gudapati

We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system d…

Global well-posedness and scattering for the defocusing, $L^{2}$ -critical, nonlinear SchrÃ¶dinger equation when $d = 1$

Benjamin Dodson

In this paper we prove that the defocusing, quintic nonlinear SchrÃ¶dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2} (R)$ . To do this…

math.AP2019

Almost sure local well-posedness and scattering for the 4D cubic nonlinear SchrÃ¶dinger equation

Benjamin Dodson, Jonas Luhrmann, Dana Mendelson

We consider the Cauchy problem for the defocusing cubic nonlinear SchrÃ¶dinger equation in four space dimensions and establish almost sure local well-posedness and conditional almo…

Global well-posedness for the radial, defocusing, nonlinear wave equation for $3 < p < 5$

Benjamin Dodson

In this paper we continue the study of the defocusing, energy-subcritical nonlinear wave equation with radial initial data lying in the critical Sobolev space. In this case we prov…

math.AP2009

Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

Benjamin Dodson

We prove global well-posedness for the cubic, defocusing, nonlinear Schr{Ã¶}dinger equation on $R^{2}$ with data $u_{0} \in H^{s} (R^{2})$ , $s > 1/4$ . We accomplis…

Sharp Global well-posedness and scattering for the radial conformal nonlinear wave equation

Benjamin Dodson

In this paper we prove global well-posedness and scattering for the conformal, defocusing, nonlinear wave equation with radial initial data in the critical Sobolev space, for dimen…

math.AP2012

Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{Ã¶}dinger equation in the exterior of a convex obstacle when $d = 4$

Benjamin Dodson

In this paper we prove that the energy - critical nonlinear Schr{Ã¶}dinger equation in the domain exterior to a convex obstacle is globally well - posed and scattering for initial…

math.AP2019

Global well-posedness and scattering for nonlinear Schr{Ã¶}dinger equations with algebraic nonlinearity when $d = 2, 3$ , $u_{0}$ radial

Benjamin Dodson

In this paper we discuss global well - posedness and scattering for some initial value problems that are $L^{2}$ supercritical and $H ˙^{1}$ subcritical, with radial data. We p…

math.AP2024

Rigidity for the non self-dual Chern--Simons--Schr{Ã¶}dinger equation at the level of the soliton

Benjamin Dodson

In this paper we prove a rigidity result for a solution to the non self-dual Chern--Simons--Schr{Ã¶}dinger equation at the level of the soliton.

math.AP2022

A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton

Benjamin Dodson

In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear Schr{Ã¶}dinger equation in dimensions $2 \leq d \leq 15$ with mass equal to the mass o…

math.AP2015

The defocusing quintic NLS in four space dimensions

Benjamin Dodson, Changxing Miao, Jason Murphy +1

We consider the defocusing quintic nonlinear SchrÃ¶dinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be g…

Global well-posedness for the logarithmically energy-supercritical Nonlinear Wave Equation with partial symmetry

Aynur Bulut, Benjamin Dodson

We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies…

Global well-posedness for the cubic nonlinear Schr{Ã¶}dinger equation with initial lying in $L^{p}$ -based Sobolev spaces

Benjamin Dodson, Avraham Soffer, Thomas Spencer

In this paper we continue our study [DSS20] of the nonlinear SchrÃ¶dinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb…

Global well-posedness for the defocusing, cubic nonlinear Schr{Ã¶}dinger equation with initial data in a critical space

Benjamin Dodson

In this note we prove global well-posedness for the defocusing, cubic nonlinear Schr{Ã¶}dinger equation with initial data lying in a critical Sobolev space.

Global well-posedness for the SchrÃ¶dinger map problem with small Besov norm

Benjamin Dodson

In this paper we prove a global result for the SchrÃ¶dinger map problem with initial data with small Besov norm at critical regularity.

astro-ph2004

Infrared Photometry of NGC 6791

Bruce W. Carney, Jae-Woo Lee, Benjamin Dodson

We present deep JHK photometry of the old and metal-rich open cluster NGC 6791. The photometry reaches below the main sequence turn-off to K = 16.5 mag. We combine our photometry w…

A determination of the blowup solutions to the focusing, quintic NLS with mass equal to the mass of the soliton

Benjamin Dodson

In this paper we prove that the only blowup solutions to the focusing, quintic nonlinear Schr{Ã¶}dinger equation with mass equal to the mass of the soliton are rescaled solitons or…

math.AP2016

Global well-posedness and scattering for the defocusing, $L^{2}$ -critical, nonlinear Schr{Ã¶}dinger equation when $d = 2$

Benjamin Dodson

In this paper we prove that the defocusing, cubic nonlinear Schr{Ã¶}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2} (R^{2})$ . To do…

Scattering for defocusing energy subcritical nonlinear wave equations

Benjamin Dodson, Andrew Lawrie, Dana Mendelson +1

We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1 + 3)$ -dimensions for energy subcritical powers $p$ in the range $3 < p < 5$ . We prove that…

math.AP2022

Global well-posedness of the radial conformal nonlinear wave equation with initial data in a critical space

Benjamin Dodson

In this note we prove global well-posedness and scattering for the conformal, defocusing, nonlinear wave equation with radial initial data in a critical Besov space. We also prove…

A new proof of scattering below the ground state for the non-radial focusing NLS

Benjamin Dodson, Jason Murphy

We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial $H ˙^{1/2}$ -critical focusing NLS. By proving an interaction Morawetz inequality, we give…