LOCAL WELL-POSEDNESS OF THE NLS EQUATION WITH THIRD ORDER DISPERSION IN NEGATIVE SOBOLEV SPACES

Miyaji Tomoyuki; Tsutsumi Yoshio

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LOCAL WELL-POSEDNESS OF THE NLS EQUATION WITH THIRD ORDER DISPERSION IN NEGATIVE SOBOLEV SPACES

机译：NLS方程的局部良好呈现，具有负面SOBOLEV空间中的第三次分散

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We show the time local well-posedness in H-s of the reduced NLS equation with third order dispersion (r3NLS) on T for s -1/6. Our proof is based on the nonlinear smoothing effect, which is similar to that for mKdV. However, when (r3NLS) is considered in Sobolev spaces of negative indices, the unconditional uniqueness of solutions, that is, the uniqueness of solutions without auxiliary spaces breaks down in marked contrast to mKdV.

机译：我们在S＆GT上显示了具有第三阶分散（R3NL）的降低的NLS方程中的H-S中局部良好的局部良好。 -1/6。我们的证据基于非线性平滑效果，类似于MKDV的非线性平滑效果。然而，当在负指数的SoboLev空间中考虑（R3NL）时，解决方案的无条件唯一性，即没有辅助空间的溶液的唯一性，与MKDV的标记对比度下降。

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《Differential and integral equations》 |2018年第2期|共22页
作者
Miyaji Tomoyuki; Tsutsumi Yoshio;
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Meiji Univ Meiji Inst Adv Stud Math Sci Nakano Ku 4-21-1 Nakano Tokyo 1648525 Japan;

Kyoto Univ Dept Math Kyoto 6068502 Japan;

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正文语种 eng
中图分类微分方程、积分方程;
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1. LOCAL WELL-POSEDNESS OF THE NLS EQUATION WITH THIRD ORDER DISPERSION IN NEGATIVE SOBOLEV SPACES [J] . Miyaji Tomoyuki, Tsutsumi Yoshio Differential and integral equations . 2018,第1a2期

机译：NLS方程的局部良好呈现，具有负面SOBOLEV空间中的第三次分散
2. LOCAL WELL-POSEDNESS IN SOBOLEV SPACES WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION [J] . Hongwei WANG 数学物理学报（英文版） . 2014,第001期

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3. Local well-posedness of the Ostrovsky, Stepanyams and Tsimring equation in Sobolev spaces of negative indices [J] . Xiangqing Zhao, Shangbin Cui Nonlinear Analysis: An International Multidisciplinary Journal . 2009,第10期

机译：负指数Sobolev空间中Ostrovsky，Stepanyams和Tsimring方程的局部适定性
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

机译：非各向同性SoboLev分数空间中R〜D×M〜k弱耦合NLS方程的系统散射
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LOCAL WELL-POSEDNESS OF THE NLS EQUATION WITH THIRD ORDER DISPERSION IN NEGATIVE SOBOLEV SPACES

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