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- W4385858069 abstract "We consider the derivative nonlinear Schrodinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and $L^2$-critical with respect to scaling. The first question we discuss is whether ensembles of orbits with $L^2$-equicontinuous initial data remain equicontinuous under evolution. We prove that this is true under the restriction $M(q)=int |q|^2 < 4pi$. We conjecture that this restriction is unnecessary. Further, we prove that the problem is globally well-posed for initial data in $H^{1/6}$ under the same restriction on $M$. Moreover, we show that this restriction would be removed by a successful resolution of our equicontinuity conjecture." @default.
- W4385858069 created "2023-08-17" @default.
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- W4385858069 date "2021-01-28" @default.
- W4385858069 modified "2023-10-18" @default.
- W4385858069 title "On the well-posedness problem for the derivative nonlinear Schrodinger equation" @default.
- W4385858069 doi "https://doi.org/10.2140/apde.2023.16.1245" @default.
- W4385858069 hasPublicationYear "2021" @default.
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