Research on propagation of singularities for nonlinear wave equations

非线性波动方程奇点传播研究

• 批准号: 14540215
• 负责人: KATO Keiichi
• 金额: $ 2.11万
• 依托单位: TOKYO UNIVERSITY OF SCIENCE
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540215/
• 关键词: nonlinear wave equation; propagation of singularity; Benjamin-Ono equation; analyticity; wellposedness; 非線形偏微分方程式; Fourier Restriction; 特異性伝播; KdV方程式; Fourier ristriction; 非線形Schrodinger方程式

1.The head investigator and co-investigator T.Ogawa has studied on the sufficient condition for solutions to the Benjamin-Ono equation to be analytic in space and time variables for t>0 with E.Kaikina and P.I.Naumkin. Under the condition that initial data have some singularity at the origin, we show that the solution is analytic for t>0.2.We have investigated the existence of solutions for the initial value problem of the Benjamin-Ono equation. However it is impossible to apply Picard's iteration method to the Benjamin-Ono equation in usual Sobolev space, we show that Picard's iteration method is applicable for some Sobolev space with homogeneous and inhomogeneous multipliers.3.We have investigate the propagation of singularities for the nonlinear wave equations with nonlinear term satisfying null condition. Regularity estimate can be improved under the null condition for nonlinear term.

1.首席研究员和共同研究员T.Okawa与E.Kaikina和P.I.Naumkin一起研究了Benjamin-Ono方程的解在t>0的空间和时间变量中解析的充分条件。在初始数据在原点具有奇异性的条件下，我们证明了t>0.2时解是解析的。我们研究了Benjamin-Ono方程初值问题解的存在性。然而Picard迭代法不可能应用于一般Sobolev空间中的Benjamin-Ono方程，我们证明了Picard迭代法适用于某些具有齐次和非齐次乘子的Sobolev空间。 3.研究了非线性方程的奇点传播非线性项满足零条件的波动方程。在非线性项为零的情况下可以改进正则性估计。

项目成果

Wellposedness and Analytic smoothing effect for the Benjamin-Ono equation

Benjamin-Ono 方程的适定性和解析平滑效应

• 发表时间: 2002
• 作者: E.Kaikina; K.Kato; P.I.Naumkin; T.Ogawa
• 通讯作者: T.Ogawa

Wellposedness and Analytic smoothing effect for the Benjamin-Ono equation

Benjamin-Ono 方程的适定性和解析平滑效应

• 发表时间: 2002
• 作者: E.Kaikina; K.Kato; P.I.Naumkin; T.Ogawa
• 通讯作者: T.Ogawa

E.Kaikina, P.I.Naumkin, K.Kato, T.Ogawa: "Wellposedness and analytic smoothing effect for the Benjamin-Ono equation"Publications of the Research Institute for Mathematical Sciences. 38・3. 651-691 (2002)

E.Kaikina、P.I.Naumkin、K.Kato、T.Okawa：“Benjamin-Ono 方程的适定性和解析平滑效应”数学科学研究所出版物 38・3（2002）。