276 citations · 4.5k across the 293 of their papers we have counts for
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A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
Michael Christ, James Colliander, Terence Tao
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces , for negative but close to 0.…
A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations
Terence Tao
We study the asymptotic behavior of large data solutions to Schrödinger equations in , assuming globally bounded norm (i.e. no blowup in the…
Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective
Terence Tao
We discuss some of the key ideas of Perelman's proof of Poincaré's conjecture via the Hamilton program of using the Ricci flow, from the perspective of the modern theory of nonline…
Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions
Terence Tao, Monica Visan, Xiaoyi Zhang
We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation for large…
Minimal-mass blowup solutions of the mass-critical NLS
Terence Tao, Monica Visan, Xiaoyi Zhang
We consider the minimal mass required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation to blow up. If is finite, we sh…
New bounds for Szemeredi's theorem, II: A new bound for
Ben Green, Terence Tao
Define to be the largest cardinality of a set in which does not contain four elements in arithmetic progression. In 1998 Gowers proved that $r_4(N) \ll…