M. Keel

activity

19992004

most citedGlobal well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3

51 citations · 54 across the 5 of their papers we have counts for

collaborators

Showing 2002Show all

3 papers · 1 filter

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

Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation

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

We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H^s(R^n) when n = 2, 3 and s > 4/7, 5/6,…