Abstract
The initial value problem for the defocusing cubic nonlinear Schrödinger equation on ${\Bbb R}^2$ is locally well-posed in Hs for s ≥ 0. The L^2-space norm is invariant under rescaling to the equation, then the critical regularity is s = 0. In this note, we prove the global well-posedness in Hs for all s > 1/2. The proof uses the almost conservation approach by adding additional (non-resonant) correction terms to the original almost conserved energy.
Citation
Hideo TAKAOKA. "Bilinear Strichartz estimates and applications to the cubic nonlinear Schrödinger equation in two space dimensions." Hokkaido Math. J. 37 (4) 861 - 870, November 2008. https://doi.org/10.14492/hokmj/1249046373
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