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We prove non-existence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the circle if initial data belong to H^s(핋)\setminus L^2(핋) for some s∈(−1/8,0). The proof is based on establishing an a priori bound on solutions to a renormalized cubic NLS in negative Sobolev spaces via the short time Fourier restriction norm method.
|Number of pages||74|
|Journal||International Mathematics Research Notices|
|Early online date||26 Dec 2016|
|Publication status||Published - 20 Mar 2018|
- nonlinear Schrödinger equation
- short time Fourier restriction norm method
- a priori estimate
- normal form reduction
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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20