The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrdinger equation

Han Wei

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The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrdinger equation

机译：四阶Schrodinger方程的尖的Strichartz和Sobolev-Strichartz不等式

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摘要

In this paper, we will obtain that there exists a maximizer for the non-endpoint Strichartz inequalities for the fourth-order Schrodinger equation with initial data in the L-2(R-d) space in all dimensions, and then we obtain a maximizer also for the non-endpoint Sobolev-Strichartz inequality for the fourth-order Schrodinger equation with initial data in the homogeneous Sobolev space. Our analysis derived from the linear profile decomposition. Copyright (c) 2014 John Wiley & Sons, Ltd.

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《Mathematical Methods in the Applied Sciences》 |2015年第8期|共9页
作者
Han Wei;
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正文语种 eng
中图分类数学;
关键词
fourth-order Schrodinger equation; Strichartz estimate; Sobolev-Strichartz inequality; maximizer;

机译：四阶Schrodinger方程Strichartz估计Sobolev-Strichartz不等式最大化;

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专利

1. The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrdinger equation [J] . Han Wei Mathematical Methods in the Applied Sciences . 2015,第8期

机译：四阶Schrodinger方程的尖的Strichartz和Sobolev-Strichartz不等式
2. The lack of compactness in the Sobolev-Strichartz inequalities [J] . Fanelli L., Visciglia N. Journal de Mathematiques Pures et Appliquees . 2013,第3期

机译：Sobolev-Strichartz不等式缺乏紧致性
3. Existence of maximizers for Sobolev-Strichartz inequalities [J] . Fanelli L., Vega L., Visciglia N. Advances in Mathematics . 2012,第3期

机译：Sobolev-Strichartz不等式的最大化子的存在
4. An Attestation on Equality between a Fourth-order Variational Inequality of the Second Kind and Boundary Value Problem of Biharmonic Equation [C] . Yiming Chen, Yuhuan Cui, Yongping Zhang, International Conference on Innovative Computing, Information and Control . 2007

机译：双态方程第二种与边值问题的四阶变分不等式等平等的证明
5. Global existence of solutions to nonlinear wave equations by weighted Strichartz inequalities. [D] . Alpay, Nimet. 2004

机译：加权Strichartz不等式对非线性波动方程解的整体存在性。
6. Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities [O] . M. Bonforte, J. Dolbeault, G. Grillo, 2010

机译：非线性快速扩散方程解通过函数不等式的急剧衰减
7. The lack of compactness in the Sobolev-Strichartz inequalities [O] . Luca Fanelli, Nicola Visciglia 2016

机译：sobolev-strichartz不等式缺乏紧凑性

The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrdinger equation

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