Abstract
We consider the time-local well-posedness for the initial-value problem of the fourth-order nonlinear Schrödinger-type equation in one space dimension which describes the motion of the vortex filament. By using the method of Fourier restriction norm introduced by Bourgain [3] and Kenig-Ponce-Vega [17]--[19], we show the time-local well-posedness in the Sobolev space $H^s(\mathbb R)$ with $s\ge1/2$ under certain coefficient conditions.
Citation
J. Segata. "Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament." Differential Integral Equations 16 (7) 841 - 864, 2003. https://doi.org/10.57262/die/1356060600
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