The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in Hs

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Abstract

In this paper, the local and global existence of solutions for the Cauchy problem of the critical and subcritical nonlinear Schrödinger equations in H^s (s ≥ 2) is studied by using the manner of formal differentiation with respect to time. Some conjectures posed by Cazenave and Weissler in [1] are verified.

Keywords:

Nonlinear Schrödinger equation;Cauchy problem;critical and subcritical powers in H^s;global existence
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The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in Hs. (1998). Journal of Partial Differential Equations, 11(2), 173-192. https://www.global-sci.com/index.php/jpde/article/view/3884