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- W2015961585 abstract "In this paper, we prove that there exists some small epsilon(*) > 0 such that the derivative nonlinear Schrodinger equation ( DNLS) is globally well-posed in the energy space, provided that the initial data u(0) is an element of H-1(R) satisfies parallel to u(0)parallel to(L2) < root 2 pi + epsilon(*). This result shows us that there are no blow-up solutions whose masses slightly exceed 2 pi, even if their energies are negative. This phenomenon is much different from the behavior of the nonlinear Schrodinger equation with critical nonlinearity. The technique used is a variational argument together with the momentum conservation law. Further, for the DNLS on the half-line R+, we show the blow-up for the solution with negative energy." @default.
- W2015961585 created "2016-06-24" @default.
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- W2015961585 date "2013-12-31" @default.
- W2015961585 modified "2023-09-23" @default.
- W2015961585 title "Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space" @default.
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- W2015961585 doi "https://doi.org/10.2140/apde.2013.6.1989" @default.
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