Global well-posedness and scattering for the fourth order nonlinear Schrodinger equations with small data in modulation and Sobolev spaces

Ruzhansky Michael; Wang Baoxiang; Zhang Hua

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Global well-posedness and scattering for the fourth order nonlinear Schrodinger equations with small data in modulation and Sobolev spaces

机译：调制空间和Sobolev空间中具有小数据的四阶非线性Schrodinger方程的整体适定性和散射

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The local well-posedness with small data in H-s (R-n) (s >= 3 + max(n/2,1(+))) for the Cauchy problem of the fourth order nonlinear Schrodinger equations with the third order derivative nonlinear terms were obtained by Huo and Jia [17]. In this paper we show its global well-posedness with small data in the modulation space M-2,1(7/2) and in Sobolev spaces Hn/2+7+/2. For a special nonlinear term containing only one third order derivative, we can show its global well posedness in M-2,1(7/2) H(n+1+)/2. (C) 2015 Elsevier Masson SAS. All rights reserved.

机译：具有三阶导数非线性项的四阶非线性Schrodinger方程Cauchy问题的Hs（Rn）（s> = 3 + max（n / 2,1（+）））中的小数据的局部适定性为由霍和贾获得[17]。在本文中，我们在调制空间M-2,1（7/2）和Sobolev空间Hn / 2 + 7 + / 2中以小数据显示了它的全局适定性。对于仅包含一个三阶导数的特殊非线性项，我们可以在M-2,1（7/2）H（n + 1 +）/ 2中显示其全局适定性。（C）2015 Elsevier Masson SAS。版权所有。

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《Journal de Mathematiques Pures et Appliquees》 |2016年第1期|共35页
作者
Ruzhansky Michael; Wang Baoxiang; Zhang Hua;
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正文语种 eng
中图分类数学;
关键词
Global well-posedness; Fourth order nonlinear Schrodinger equations; Small initial data; Modulation and Sobolev spaces;

机译：全局适定性;四阶非线性Schrodinger方程;小的初始数据;调制和Sobolev空间;

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1. Global well-posedness and scattering for the fourth order nonlinear Schrodinger equations with small data in modulation and Sobolev spaces [J] . Ruzhansky Michael, Wang Baoxiang, Zhang Hua Journal de Mathematiques Pures et Appliquees . 2016,第1期

机译：调制空间和Sobolev空间中具有小数据的四阶非线性Schrodinger方程的整体适定性和散射
2. Well-posedness of Cauchy problem of fourth-order Schrodinger equations in anisotropic Sobolev space [J] . Guo CH, Cui SB Applied mathematics and computation . 2007,第1期

机译：各向异性Sobolev空间中四阶Schrodinger方程的Cauchy问题的适定性
3. Well-posedness of higher-order nonlinear Schrodinger equations in Sobolev spaces Hs(Rn) and applications [J] . Shangbin Cui, Cuihua Guo Nonlinear Analysis: An International Multidisciplinary Journal . 2007,第3期

机译：Sobolev空间Hs（Rn）中高阶非线性Schrodinger方程的适定性及其应用
4. Scattering for systems of N weakly coupled NLS equations on R~d × M~k in non-isotropic Sobolev fractional spaces [C] . Mirko Tarulli, George Venkov International Conference on Applications of Mathematics in Engineering and Economics . 2018

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5. Global well-posedness and parametrices for critical Maxwell-Dirac and massive Maxwell-Klein-Gordon equations with small Sobolev data [D] . Gavrus, Cristian Dan. 2017

机译：具有小SOBOLEV数据的临界麦克斯韦尔 - DIRAC和MASHWELWELL-KLEIN-GORNON方程的全球良好的姿势和参数
6. Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity [O] . Liejun Shen -1

机译：具有Hardy-Sobolev指数和奇异非线性的Kirchhoff型方程解的多重性和渐近性
7. Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces [O] . Ruzhansky, M, Wang, B, Zhang, H 2015

机译：调制和sobolev空间中具有小数据的四阶非线性schrödinger方程的全局适定性和散射

Global well-posedness and scattering for the fourth order nonlinear Schrodinger equations with small data in modulation and Sobolev spaces

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