LOW REGULARITY FOR A QUADRATIC SCHRODINGER EQUATION ON T

Thomann L

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LOW REGULARITY FOR A QUADRATIC SCHRODINGER EQUATION ON T

机译：T上的二次Schrodinger方程的低正则性

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In this paper we consider a Schrodinger equation on the circle with a quadratic nonlinearity. Thanks to an explicit computation of the first Picard iterate, we give a better description of the dynamic of the solution, whose existence was proved by C. E. Kenig, G. Ponce and L. Vega [15]. We also show that the equation is well posed in a space H(s,p)(T) which contains the Sobolev space H(s)(T) when p >= 2.

机译：在本文中，我们考虑具有二次非线性的圆上的薛定inger方程。多亏了第一个Picard迭代的显式计算，我们对解的动力学有了更好的描述，C。E. Kenig，G。Ponce和L. Vega证明了其存在[15]。我们还表明，当p> = 2时，方程很好地摆在包含Sobolev空间H（s）（T）的空间H（s，p）（T）中。

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来源
《Differential and integral equations》 |2011年第12期|共20页
作者
Thomann L;
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正文语种 eng
中图分类微分方程、积分方程;
关键词
SCHRODINGER; consider; Schrodinger;

机译：SCHRODINGER;考虑;Schrodinger;

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1. WELL-POSEDNESS AND SCATTERING FOR A SYSTEM OF QUADRATIC DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS WITH LOW REGULARITY INITIAL DATA [J] . Hirayama Hiroyuki Communications on pure and applied analysis . 2014,第4期

机译：低初始数据的二次导数非线性Schrodinger方程系统的适定性和散射
2. Low regularity solutions for a 2D quadratic nonlinear Schrodinger equation [J] . Bejenaru I, De Silva D Transactions of the American Mathematical Society . 2008,第11期

机译：二维二次非线性Schrodinger方程的低正则解
3. Low Regularity Exponential-Type Integrators for Semilinear Schrodinger Equations [J] . Ostermann Alexander, Schratz Katharina Foundations of computational mathematics . 2018,第3期

机译：Semilinear Schrodinger方程的低规律性指数型积分器
4. Energy Estimates for Low Regularity Bilinear Schrodinger Equations [C] . Nabile Boussaid, Marco Caponigro, Thomas Chambrion IFAC Workshop on Control of Systems Governed by Partial Differential Equations . 2014

机译：低规律性Bilinear Schrodinger方程的能量估计
5. Low Regularity Solutions of Korteweg-de Vries and Chern-Simons-Schrodinger Equations. [D] . Liu, Baoping. 2012

机译：Korteweg-de Vries和Chern-Simons-Schrodinger方程的低正则解。
6. Global Weak Rigidity of the Gauss–Codazzi–Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity [O] . Gui-Qiang G. Chen, Siran Li -1

机译：高斯-科达兹-里奇方程的整体弱刚度和低规则性的黎曼流形的等距浸入
7. WELL-POSEDNESS AND SCATTERING FOR A SYSTEM OF QUADRATIC DERIVATIVE NONLINEAR SCHRÖDINGER EQUATIONS WITH LOW REGULARITY INITIAL DATA [O] . Hiroyuki Hirayama 2016

机译：具有低正则初始数据的二次导数非线性schrödinger方程组的良好可能性和散射

LOW REGULARITY FOR A QUADRATIC SCHRODINGER EQUATION ON T

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