T. Tao

activity

19982008

most citedIll-posedness for nonlinear Schrodinger and wave equations

119 citations · 600 across the 52 of their papers we have counts for

collaborators

Showing 2002 · math.APShow all

3 papers · 2 filters

math.AP2002

Polynomial upper bounds for the instability of the Nonlinear Schrödinger equation below the energy norm

J. Colliander, M. Keel, G. Staffilani +2

We continue the study (initiated in \cite{ckstt:7}) of the orbital stability of the ground state cylinder for focussing non-linear Schrödinger equations in the $H^{s} (R^{n})$ norm for…

math.AP2002★ 1 cited

Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm

Jim Colliander, Mark Keel, Gigliola Staffilani +2

We study the long-time behaviour of the focusing cubic NLS on $R$ in the Sobolev norms $H^{s}$ for $0 < s < 1$ . We obtain polynomial growth-type upper bounds on the $H^{s}$ norms, and…

math.AP2002

Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions

Andrew Hassell, Terence Tao

Suppose that $M$ is a compact Riemannian manifold with boundary and $u$ is an $L^{2}$ -normalized Dirichlet eigenfunction with eigenvalue $λ$ . Let $ψ$ be its normal derivative at the…