Abstract
We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schrödinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schrödinger equation (DNLS). For (DNLS), Wu (2015) proved that the solution with the initial data is global if by the sharp Gagliardo–Nirenberg inequality. The variational argument gives us another proof of the global existence for (DNLS). Moreover, by the variational argument, we can show that the solution to (DNLS) is global if the initial data satisfies and the momentum is negative.
Citation
Noriyoshi Fukaya. Masayuki Hayashi. Takahisa Inui. "A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation." Anal. PDE 10 (5) 1149 - 1167, 2017. https://doi.org/10.2140/apde.2017.10.1149
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