Almost sure well-posedness of the cubic nonlinear Schr\
By James E. Colliander, Tadahiro Oh. 2009
165 citations recorded by the source corpus.
We consider the Cauchy problem for the one-dimensional periodic cubic non- linear Schrodinger equation (NLS) with initial data below L 2 . In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well- posedness of NLS almost surely for the initial data in the support of the canonical Gaussian measures on H s (T) for each s > − 1 , and global well-posedness for each s > − 1 12 .
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0a1810e58c7dee41e116a7b49df2404d33a833c5
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In Applied Mathematics
In Mathematical Physics
- D. Mendelson
- Gigliola Staffilani
- Jonas Lührmann
- Andrea R. Nahmod
- D. Tataru
- Tadahiro Oh
- Terence Tao
- Oana Pocovnicu
Citations in the corpus
- Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\"odinger equation below the energy space (2013, methodology): “Colliander and Oh [17] also proved almost sure global well-posedness for the subcritical 1D periodic cubic NLS below L2 in the absence of invariant measures by suitably adapting Bourgain’s high-low method.”
- Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ3 (2014, background): “Colliander and Oh [14] adapt Bourgain’s high-low frequency decomposition [6] to prove almost sure global existence of solutions to the one-dimensional periodic defocusing cubic nonlinear Schrödinger equation below L2 .”