| 研究課題/領域番号 |
15K17570
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| 研究種目 |
若手研究(B)
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| 配分区分 | 基金 |
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| 研究分野 |
数学解析
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| 研究機関 | 名古屋大学 |
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研究代表者 |
Roy Tristan 名古屋大学, 高等研究院(多元), 特任助教 (80751073)
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| 研究期間 (年度) |
2015-04-01 – 2019-03-31
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| 研究課題ステータス |
中途終了 (2018年度)
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| 配分額 *注記 |
3,640千円 (直接経費: 2,800千円、間接経費: 840千円)
2017年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
2016年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
2015年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
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| キーワード | dispersive equations / global well-posedness / scattering / local well-posednes / loglog supercritical / local well-posedness / third-order nonlinearity / Dispersive equations / Global existence / Scattering / Schrodinger / Wave, Klein-Gordon / Local well-posedness / Fully nonlinear problems / Asymptotic behavior / Solilton conjecture / Local behavior / Fully nonlinear PDEs |
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| 研究実績の概要 |
I worked on several problems. I proved global existence and scattering of nonsmooth solutions of some barely supercritical Schrodinger equations with a defocusing (i.e repulsive) nonlinearity: this lead to a paper recently published in International Mathematics Research Notices. I also proved global existence and scattering of smooth and nonsmooth solutions below ground state of some size-dependent barely supercritical Schrodinger equations with a focusing (i.e attractive) nonlinearity: this lead to a preprint (arXiv:1701.02689). I also worked on a problem with Prof Kotaro Tsugawa (Nagoya University and Chuo University) that involves the construction of local smooth solutions of fully nonlinear equations that satisfy
a dispersive property in a weak sense. This collaboration is about to lead to a preprint.
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