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  1. (, International Mathematics Research Notices)
    Abstract 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 dimensions $$d \geq 4$$. This result extends a previous result proving sharp scattering in the three dimensional case. 
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  2. (, International Mathematics Research Notices)
    Abstract In this note, we prove scattering for a defocusing nonlinear Schrödinger equation with initial data lying in a critical Besov space. In addition, we obtain polynomial bounds on the scattering size as a function of the critical Besov norm. 
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  3. (, Advances in Mathematics)
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  4. (, American Journal of Mathematics)
    abstract: 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 prove scattering in the critical norm when $3<5$. 
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  5. (, Proceedings of the American Mathematical Society)
    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 ∞<#comment/> L x 2 L_{t}^{\infty } L_{x}^{2} and L t ∞<#comment/> H ˙<#comment/> 2 L_{t}^{\infty } \dot {H}^{2} norms of the solution to the quintic problem. The main motivation for this paper is the use of an interaction Morawetz estimate for the nonlinear wave equation. 
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  6. (, Analysis & PDE)
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  7. (, Discrete and Continuous Dynamical Systems)
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  8. (, Annals of PDE)
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  9. (, Nonlinear Analysis)
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  10. (, Revista Matemática Iberoamericana)
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