Low regularity local well-posedness of the derivative nonlinear Schrodinger equation with periodic initial data

Grunrock A; Herr S

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Low regularity local well-posedness of the derivative nonlinear Schrodinger equation with periodic initial data

机译：具有周期初始数据的导数非线性Schrodinger方程的低正则局部适定性

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The Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition is considered. Local well-posedness for data u(0) in the space (H) over cap T-s((r)), the norms parallel to u(0)parallel to((H)) over cap (s)(r) (T) = parallel to (s) (u) over cap (0)parallel to l(xi)(r),(') is shown in the parameter range s >= 1/2, 2 > r > 4/3. The proof is based on an adaptation of the gauge transform to the periodic setting and an appropriate variant of the Fourier restriction norm method.

机译：考虑具有周期边界条件的微分非线性薛定inger方程的柯西问题。上限Ts（（r））上的空间（H）中数据u（0）的局部适定性，平行于u（0）的范数平行于上限（s）（r）上的（（H））（T ）=与上限（0）平行于（s）（u），平行于l（xi）（r），（'）显示在参数范围s> = 1/2，2> r> 4 / 3。该证明是基于规范变换对周期设置的适应以及傅立叶约束范数方法的适当变体。

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《SIAM Journal on Mathematical Analysis》 |2008年第6期|共31页
作者
Grunrock A; Herr S;
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正文语种 eng
中图分类数学分析;
关键词
local well-posedness; derivative nonlinear Schrodinger equation; periodic functions; sharp multilinear estimates; gauge transformation; generalized Fourier restriction norm method; SPACE; 1D;

机译：局部适定性;导数非线性Schrodinger方程;周期函数;尖锐的多线性估计;量规变换;广义傅里叶约束范数法;SPACE;1D;

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1. Low regularity local well-posedness of the derivative nonlinear Schrodinger equation with periodic initial data [J] . Grunrock A, Herr S SIAM Journal on Mathematical Analysis . 2008,第6期

机译：具有周期初始数据的导数非线性Schrodinger方程的低正则局部适定性
2. Well-Posedness for a System of Quadratic Derivative Nonlinear Schrodinger Equations with Radial Initial Data [J] . Hirayama Hiroyuki, Kinoshita Shinya, Okamoto Mamoru Annales Henri Poincare . 2020,第8期

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5. Well-posedness and regularity for a higher order periodic mKdV equation. [D] . Schlotthauer-Hannah, Heather. 2007

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6. EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR EQUATIONS OF EVOLUTION [O] . Felix E. Browder 1965

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7. Low regularity local well-posedness of the Derivative Nonlinear Schr"odinger Equation with periodic initial data [O] . Grünrock, A., Herr, S. 2007

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Low regularity local well-posedness of the derivative nonlinear Schrodinger equation with periodic initial data

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