A Refined Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation Related to the Vortex Filament
- 23 October 2007
- journal article
- research article
- Published by Informa UK Limited in Communications in Partial Differential Equations
- Vol. 32 (10), 1493-1510
- https://doi.org/10.1080/03605300701629385
Abstract
The Cauchy problem of one dimensional fourth-order nonlinear Schrödinger equation related to the vortex filament is studied. Local well-posedness for initial data in H s (ℝ) (s > 1/2) is obtained without conditions ν < 0 and μ − ν/2 = 0 by the Fourier restriction norm method. The result is a refinement of our previous paper (Huo and Jia, 2005 Huo , Z. , Jia , Y. ( 2005 ). The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament . J. Diff. Eq. 214 : 1 – 35 . [Google Scholar] ).Keywords
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