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Global rough solutions to the cubic nonlinear Boussinesq equation
 Journal of the London Mathematical Society
"... We prove that the initial value problem (IVP) for the cubic defocusing nonlinear Boussinesq equation utt−uxx+uxxxx − (u2u)xx = 0 on the real line is globally wellposed in Hs(R) provided 2/3 < s < 1. 1 ..."
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We prove that the initial value problem (IVP) for the cubic defocusing nonlinear Boussinesq equation utt−uxx+uxxxx − (u2u)xx = 0 on the real line is globally wellposed in Hs(R) provided 2/3 < s < 1. 1
Longtime Sobolev stability for small solutions of quasilinear KleinGordon
"... equations on the circle ..."
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Low regularity global wellposedness for the twodimensional Zakharov system
, 2009
"... The twodimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L 2norm of the Schrödinger part is small enough. The proof uses a refined Imethod originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for ..."
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The twodimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L 2norm of the Schrödinger part is small enough. The proof uses a refined Imethod originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.
RESONANT DECOMPOSITION AND THE IMETHOD FOR THE Twodimensional Zakharov System
, 2012
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iii Table of Contents
, 2008
"... Global analysis of the defocusing cubic wave equation in dimension 3 ..."
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