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^*

^*Corresponding author for this work

School of Mathematics and Statistics

China Academy of Engineering Physics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1321-1333
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	36
Issue number	11
DOIs	https://doi.org/10.1002/mma.2684
Publication status	Published - 30 Jul 2013

Keywords

fourth-order Schrödinger equation
local well-posedness
multilinear estimates

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10.1002/mma.2684

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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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AU - Zheng, Jiqiang

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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.

KW - fourth-order Schrödinger equation

KW - local well-posedness

KW - multilinear estimates

UR - https://www.scopus.com/pages/publications/84879411882

U2 - 10.1002/mma.2684

DO - 10.1002/mma.2684

M3 - Article

AN - SCOPUS:84879411882

SN - 0170-4214

VL - 36

SP - 1321

EP - 1333

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 11

ER -

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

Abstract

Keywords

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