Abstract
The paper discusses a class of quasilinear Schrödinger equations describing the upper-hybrid oscillation propagation. By establishing a cross-constrained variational problem and a so-called invariant flow, we obtain a sharp condition for blow-up and global existence of solutions of the Cauchy problem.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 2, pp. 68–74, 2008
Original Russian Text Copyright © J. Zhang and J. Shu
Supported in part by the National Natural Science Foundation of China (nos. 10747148 and 10771151) and the Scientific Research Fund of Sichuan Provincial Education Department.
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Zhang, J., Shu, J. Sharp conditions of global existence for the quasilinear Schrödinger equation. Funct Anal Its Appl 42, 135–140 (2008). https://doi.org/10.1007/s10688-008-0019-1
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DOI: https://doi.org/10.1007/s10688-008-0019-1