Benjamin Dodson

Associate Professor

Department of Mathematics 

Johns Hopkins University 

Baltimore, MD 21218 

Office: Krieger 214 

Phone: (410) 516-7472 

Email: dodson@math.jhu.edu 

 

Papers: This is a list of research papers that are now published, with links to the paper.

Infrared Photometry of NGC 6791 (with Bruce Carney and Jae - Woo Lee)

Global existence for some radial, low regularity nonlinear Schrodinger equations

Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

Global well – posedness for the defocusing, quintic nonlinear Schrodinger equation in one dimension for low regularity data

Global well – posedness and scattering for the defocusing, L2 – critical nonlinear Schrodinger equation when d ≥ 3


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

Scattering for the radial 3D cubic wave equation (with Andrew Lawrie)

A controlling norm for energy – critical Schrodinger maps (with Paul Smith)

Global well – posedness and scattering for the mass – critical nonlinear Schrodinger equation with mass below the mass of the ground state

Scattering for radial, semi – linear super – critical wave equations with bounded critical norm (with Andrew Lawrie)


Global well – posedness and scattering for the defocusing, L2 – critical nonlinear Schrodinger equation when d = 1

Global well – posedness and scattering for the defocusing, L2 – critical nonlinear Schrodinger equation when d = 2

The defocusing quintic NLS in four space dimensions (with Changxing Miao, Jason Murphy, and Jiqiang Zheng)

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

On scattering for small data of 2+1 dimensional equivariant Einstein-wave map system (with Nishanth Gudapati)


A new proof of scattering below the ground state for the 3D radial focusing cubic NLS (with Jason Murphy)


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


The profile decomposition for the hyperbolic Schrodinger equation (with Jeremy Marzuola, Benoit Pausader, and Daniel Spirn)


A new proof of scattering below the ground state for the non-radial focusing NLS (with Jason Murphy)


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



Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrodinger equation (with Jonas Luhrmann and Dana Mendelson)


Global well-posedness and scattering for the focusing, cubic Schrodinger equation in dimension d = 4


Global well-posedness and scattering for nonlinear Schrodinger equations with algebraic nonlinearity when d = 2, 3 and u_{0} is radial


Global well-posedness for the defocusing, cubic, nonlinear wave equation in three dimensions for radial initial data in H^{s} \times H^{s – 1}, s > ½.


Scattering below the ground state for the 2d radial nonlinear Schrodinger equation (with Anudeep Kumar Arora and Jason Murphy)



Almost sure scattering for the 4d energy-critical defocusing nonlinear wave equation with radial data (with Jonas Luhrmann and Dana Mendelson)


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



Arxiv preprints may be found here



Book:

Defocusing nonlinear Schrödinger equations


PhD Thesis: 

Caustics and the indefinite signature Schrödinger equation, linear and nonlinear



Keynote presentation:


Scattering for the defocusing, cubic nonlinear wave equation


 

Teaching

 

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