Multilinear estimates and well-posedness for the vortex filament fourth-order Schrödinger equations

Junyong Zhang; Jiqiang Zheng

doi:10.1002/mma.2684

Multilinear estimates and well-posedness for the vortex filament fourth-order Schrödinger equations

Junyong Zhang, Jiqiang Zheng^*

^*此作品的通讯作者

数学学院

China Academy of Engineering Physics

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

This paper is concerned with the initial value problem for the fourth-order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth-order Schrödinger through the [k,Z]-multiplier norm method. we establish multilinear estimates for this nonlinear fourth-order Schrödinger type equation. The local well-posedness for initial data in ℍ^s(R) with s > 1/2 is implied by the multilinear estimates.

源语言	英语
页（从-至）	1321-1333
页数	13
期刊	Mathematical Methods in the Applied Sciences
卷	36
期	11
DOI	https://doi.org/10.1002/mma.2684
出版状态	已出版 - 30 7月 2013

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abstract = "This paper is concerned with the initial value problem for the fourth-order nonlinear Schr{\"o}dinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth-order Schr{\"o}dinger through the [k,Z]-multiplier norm method. we establish multilinear estimates for this nonlinear fourth-order Schr{\"o}dinger type equation. The local well-posedness for initial data in ℍs(R) with s > 1/2 is implied by the multilinear estimates.",

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N2 - This paper is concerned with the initial value problem for the fourth-order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth-order Schrödinger through the [k,Z]-multiplier norm method. we establish multilinear estimates for this nonlinear fourth-order Schrödinger type equation. The local well-posedness for initial data in ℍs(R) with s > 1/2 is implied by the multilinear estimates.

AB - This paper is concerned with the initial value problem for the fourth-order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth-order Schrödinger through the [k,Z]-multiplier norm method. we establish multilinear estimates for this nonlinear fourth-order Schrödinger type equation. The local well-posedness for initial data in ℍs(R) with s > 1/2 is implied by the multilinear estimates.

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Multilinear estimates and well-posedness for the vortex filament fourth-order Schrödinger equations

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