GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE FOCUSING, CUBIC SCHRODINGER EQUATION IN DIMENSION d=4

Dodson Benjamin

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GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE FOCUSING, CUBIC SCHRODINGER EQUATION IN DIMENSION d=4

机译：全球良好的姿势和散射，尺寸下的立方薛定格格方程，D = 4

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In this paper we prove global well-posedness and scattering for the focusing, cubic Schrodinger equation in four dimensions below the ground state. Previous work proved this in five dimensions and higher. To prove this, we combine the double Duhamel method with the long time Strichartz estimates.

机译：在本文中，我们证明了全球良好的朝向聚焦和散射，在地面下方的四个尺寸中的聚焦，立方Schrodinger方程。以前的工作证明这五个维度和更高。为了证明这一点，我们将双Duhamel方法与长时间的Strichartz估计相结合。

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《Annales scientifiques de l'Ecole normale superieure》 |2019年第1期|共42页
作者
Dodson Benjamin;
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Johns Hopkins Univ Dept Math Krieger 214 Baltimore MD 21218 USA;

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正文语种 eng
中图分类自然科学总论;师范教育理论;
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1. GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE FOCUSING, CUBIC SCHRODINGER EQUATION IN DIMENSION d=4 [J] . Dodson Benjamin Annales scientifiques de l'Ecole normale superieure . 2019,第1期

机译：全球良好的姿势和散射，尺寸下的立方薛定格格方程，D = 4
2. Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrodinger equation for radial data in high dimensions [J] . Tao T, Visan M, Zhang XY Duke mathematical journal . 2007,第1期

机译：高维径向数据的散焦质量临界非线性Schrodinger方程的整体适定性和散射
3. Global Well-posedness and Scattering for the Defocusing Cubic nonlinear Schrödinger equation in Four Dimensions [J] . Monica Vişan Int Math Res Notices . 2012,第5期

机译：四维散焦三次非线性Schrödinger方程的整体适定性和散射
4. Uniform asymptotic of solution of the cubic nonlinear Schrodinger equation in the focal area of the narrow 2-dimensional focused light beam [C] . Proekt, L.B., Tropp, . 1997

机译：二维二维聚焦光束聚焦区域中三次非线性薛定inger方程解的一致渐近
5. Global behavior of finite energy solutions to the focusing nonlinear Schrodinger equation in d dimension. [D] . Guevara, Cristi Darley. 2011

机译：d维聚焦非线性Schrodinger方程的有限能量解的整体行为。
6. One class of meromorphic solutions of general two-dimensional nonlinear equations connected with the algebraic inverse scattering method [O] . D. V. Chudnovsky 1978

机译：一类一般的二维非线性方程的亚纯解与代数逆散射法联系起来
7. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case [O] . Kenig, Carlos E., Merle, Frank 2006

机译：对能源至关重要的全球适应性，分散和爆炸，聚焦，径向情形下的非线性薛定谔方程

GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE FOCUSING, CUBIC SCHRODINGER EQUATION IN DIMENSION d=4

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