Bilinear Strichartz estimates and applications to the cubic nonlinear Schrödinger equation in two space dimensions
TAKAOKA, Hideo
Hokkaido Math. J., Tome 37 (2008) no. 4, p. 861-870 / Harvested from Project Euclid
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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.
Publié le : 2008-11-15
Classification:  Strichartz estimate,  nonlinear Schrödinger equation,  global well-posedness,  35Q55 
@article{1249046373,
     author = {TAKAOKA, Hideo},
     title = {Bilinear Strichartz estimates and applications to the cubic nonlinear Schr\"odinger equation in two space dimensions},
     journal = {Hokkaido Math. J.},
     volume = {37},
     number = {4},
     year = {2008},
     pages = { 861-870},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046373}
}

TAKAOKA, Hideo. Bilinear Strichartz estimates and applications to the cubic nonlinear Schrödinger equation in two space dimensions. Hokkaido Math. J., Tome 37 (2008) no. 4, pp.  861-870. http://gdmltest.u-ga.fr/item/1249046373/