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- Benjamin Dodson
- 2015

In this paper we prove that the focusing, d-dimensional mass critical nonlinear Schrödinger initial value problem is globally well-posed and scattering for u0 ∈ L 2(Rd), ‖u0‖L2(Rd) < ‖Q‖L2(Rd), where… (More)

We revisit the scattering result of Holmer and Roudenko [5] on the radial focusing cubic NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz estimate, we give a… (More)

- Benjamin Dodson
- 2012

In this talk we study the defocusing, L2 critical initial value problem iut + ∆u = |u|u, u(0, x) = u0 ∈ L(R). (1) We prove (??) is globally well-posed and scattering for all u0 ∈ L2(Rd). The… (More)

We consider the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^4$ and establish almost sure global existence and scattering for randomized radially symmetric initial data in… (More)

- Benjamin Dodson
- 2016

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 Ḣ 1 2 × Ḣ− 1 2 (R) and subcritical with… (More)

- Benjamin Dodson
- 2016

- Benjamin Dodson
- 2017

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

We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial Ḣ1/2-critical focusing NLS. By proving an interaction Morawetz inequality, we give a simple proof of scattering… (More)

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 model target… (More)