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Dispersive and Strichartz estimates for Schrodinger equations
https://doi.org/10.15083/00004045
https://doi.org/10.15083/0000404513790ba5-3def-4a02-bf89-904846c27c2b
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MIzutaniH_23_3_PhD_a.pdf (2.5 MB)
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MIzutaniH_23_3_PhD_b.pdf (71.2 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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公開日 | 2012-10-23 | |||||
タイトル | ||||||
タイトル | Dispersive and Strichartz estimates for Schrodinger equations | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | Strichartz estimate | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Dispersive estimate | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Asymptotic expansion | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Schriidinger equation | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Scattering manifold. | |||||
主題Scheme | Other | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_46ec | |||||
タイプ | thesis | |||||
ID登録 | ||||||
ID登録 | 10.15083/00004045 | |||||
ID登録タイプ | JaLC | |||||
その他のタイトル | ||||||
その他のタイトル | シュレディンガー方程式に対する分散型及びストリッカーツ評価 | |||||
著者 |
MIzutani, Haruya
× MIzutani, Haruya |
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著者別名 | ||||||
識別子 | 9353 | |||||
識別子Scheme | WEKO | |||||
姓名 | 水谷, 治哉 | |||||
著者所属 | ||||||
著者所属 | 東京大学大学院数理科学研究科 | |||||
著者所属 | ||||||
著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
Abstract | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | The present paper is concerned with LP -smoothing properties of solutions to time dependentSchriidinger equations. Vve study two kinds of V-smoothing properties, namely theStrichar:f;z estimates and the dispersive estimates.The first part is concerned with Strichartz estimates for Schriidinger equations onscattering manifolds which are non-compact manifolds with asymptotically conic ends.It is shown that time-local Strichartz estimates, outside a large compact set centered atorigin, hold for any admissible pair (including the endpoint). Moreover, we prove globalin space Strichartz estimates under the nontrapping condition of the geodesic flow. \¥ealso study a relationship between Strichartz estimates and microlocal properties of thesolution. More precisely, it is shown that (local in time) Strichartz estimates follow fromthe dispersive estimates for spatial and frequency localized solutions. This part is basedon a paper " Strichartz estimates for Schriidinger equations on scattering manifolds " .The second part is concerned with dispersive estimates for scattering solutions toone-dimensional Schriidinger equations with potentials. We prove a weighted dispersiveestimate for the non-resonant state with stronger time decay than the case of the usualunweighted estimate. Furthermore asymptotic expansions in time of scattering solutionsare given. This part is based on a paper "Dispersive estimates and asymptotic expansionsfor Schriidinger equations in dimension one" to appear in Journal of the MathematicalSociety ofJapan. | |||||
書誌情報 | 発行日 2011-03-24 | |||||
日本十進分類法 | ||||||
主題 | 410 | |||||
主題Scheme | NDC | |||||
学位名 | ||||||
学位名 | 博士(数理科学) | |||||
学位 | ||||||
値 | doctoral | |||||
学位分野 | ||||||
Mathematical Sciences (数理科学) | ||||||
学位授与機関 | ||||||
学位授与機関名 | University of Tokyo (東京大学) | |||||
研究科・専攻 | ||||||
Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
学位授与年月日 | ||||||
学位授与年月日 | 2011-03-24 | |||||
学位授与番号 | ||||||
学位授与番号 | 甲第27194号 | |||||
学位記番号 | ||||||
博数理第375号 |