Geodesic
Sharp Conditions of Global Existence for the Quasilinear Schr\"{o}dinger Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 68-74

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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.
Keywords: quasilinear Schrödinger equation, blow-up, sharp condition.
Mots-clés : global existence 
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     author = {J. Zhang and J. Shu},
     title = {Sharp {Conditions} of {Global} {Existence} for the {Quasilinear} {Schr\"{o}dinger} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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J. Zhang; J. Shu. Sharp Conditions of Global Existence for the Quasilinear Schr\"{o}dinger Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 68-74. http://geodesic.mathdoc.fr/item/FAA_2008_42_2_a7/