276 citations · 4.5k across the 293 of their papers we have counts for
11 papers · 2 filters
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…
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…
A counterexample to an endpoint bilinear Strichartz inequality
Terence Tao
The endpoint Strichartz estimate is known to be false by the work of Montgomery-Smith, despite bei…
Global behaviour of nonlinear dispersive and wave equations
Terence Tao
We survey recent advances in the analysis of the large data global (and asymptotic) behaviour of nonlinear dispersive equations such as the nonlinear wave (NLW), nonlinear Schrödin…
Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data
Terence Tao
We establish global regularity for the logarithmically energy-supercritical wave equation in three spatial dimensions for spherically symmetric initial d…
A pseudoconformal compactification of the nonlinear Schrödinger equation and applications
Terence Tao
We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schrödinger…
Two remarks on the generalised Korteweg de-Vries equation
Terence Tao
We make two observations concerning the generalised Korteweg de Vries equation . Firstly we give a scaling argument that shows, roughly speaking,…
Scattering for the quartic generalised Korteweg-de Vries equation
Terence Tao
We show that the quartic generalised KdV equation is globally wellposed for data in the critical (scale-invariant) space with…
Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions
Terence Tao
Results of Struwe, Grillakis, Struwe-Shatah, Kapitanski, Bahouri-Shatah, Bahouri-Gérard and Nakanishi have established global wellposedness, regularity, and scattering in the energ…