191 citations · 403 across the 17 of their papers we have counts for
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Almost global existence for quasilinear wave equations in three space dimensions
M. Keel, H. Smith, C. D. Sogge
We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski sp…
Multilinear estimates for periodic KdV equations and applications
Jim Colliander, Markus Keel, Gigliola Staffilani +2
We prove an endpoint multilinear estimate for the spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for perio…
A refined global well-posedness result for Schrodinger equations with derivative
J. Colliander, M. Keel, G. Staffilani +2
In this paper we prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in , for for data small in . To under…
Almost global existence for some semilinear wave equations
Markus Keel, Hart Smith, Christopher D. Sogge
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euc…
Global well-posedness for Schrödinger equations with derivative
J. Colliander, M. Keel, G. Staffilani +2
We prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in , for for small data. The result follows from an ap…
Global well-posedness for KdV in Sobolev Spaces of negative index
J. Colliander, M. Keel, G. Staffilani +2
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial…