Researchers Database
OGAWA Masao
| Faculty | Mathematics and Natural Sciences |
|---|---|
| Position | Associate Professor |
| HomepageURL | |
| Birthday |
Last Updated :2025/04/12
Researcher Information
Degree
J-Global ID
Profile
- 1
Research Areas
- Natural sciences / Mathematical physics and basic theory
- Natural sciences / Applied mathematics and statistics
- Natural sciences / Basic mathematics
Education
- - 2003 Keio University Graduate School of Science and Technology School of Fundamental Science and Technology
- - 2003 Keio University Graduate School of Science and Technology School of Fundamental Science and Technology
- - 1997 Keio University Faculty of Science and Technology Department of Mathematics
- - 1997 Keio University Faculty of Science and Engineering Department of Mathematics
Published Papers
- Effects of the Viscosity on the Linear Instability of the Toroidal Rim on a Liquid SheetOGAWA Masao兵庫教育大学研究紀要 56 181 - 188 2020/02 [Refereed]
- Evolution of Toroidal Free-Rim Perturbations on an Expanding Circular Liquid Sheet小川 聖雄Experiments in Fluids 59:148 1 - 18 2018/09 [Refereed]
Research Grants & Projects
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2020/04 -2024/03Author : 小池 敏司; 小川 聖雄本研究における前半の第一目標は、ナッシュ多様体間のナッシュ写像（つまり、実代数的写像）に対するナッシュ構造安定性問題の解決に努めることにある。つまり、ナッシュ構造安定性に対する結構次元（安定な写像全体が写像空間内で開かつ稠密になる多様体の次元の対）を決定することにある。本研究で試みているのは、写像の定義域のナッシュ多様体がコンパクトの場合に、近年、塩田昌弘氏達によって決定されている実解析構造安定性の結構次元にナッシュ構造安定性の結構次元が一致することを示すことである。この問題に関する当該年度の研究成果は、実解析構造安定性の結構次元はナッシュ構造安定性の結構次元になっていることを示したことである。 滑らかなコンパクト多様体から滑らかな多様体への滑らかな写像に対する構造安定性定理を示す上で非常に重要な役割を果たす概念に、R. Thom によって導入された「ジェットの十分性」と呼ばれるものがある。この概念に関連し、研究協力者の K. Bekka 氏と相対ジェットの V-十分性と C^0-十分性に対する相対 Kuo 条件と呼ぶ特徴付けを与えていた。この相対 Kuo 条件に対し、いくつかの同値条件を見つけたので、それらを一つの論文にまとめて欧州の雑誌より出版した。 本研究における後半の目標は、実解析多様体間の実解析写像に対する部分解析的構造安定性問題の解決に努めることにある。この問題に関連し、研究協力者の L. Paunescu 氏と部分解析的集合に対する幾何学的方向束の安定化問題に取り組み解決し、この結果を論文にまとめていたが、その論文を欧州の雑誌より出版した。
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2008 -2009Author : OGAWA MasaoThe motion of water waves is a prime research subject in fluid dynamics. This motion is usually formulated as the free boundary problem for an irrotational, incompressible and ideal fluid. It is known that the temporally local solution for this problem exists, even if the waves overhang. On the other hand, the motion of the waves of the ocean is rotational. Therefore, we are interested in the water-wave problem without the assumption of the irrotational motion. First, the author has analyzed the linearized problem. This problem is different from the one in the case that the amplitude of the surface is not large. After that, by the result for the linearized problem and the symmetry of the equations, the existence of the temporally local solution for the water-wave problem has been shown.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2007 -2009Author : USHIJIMA Takeo; ISHIWATA Tetsuya; YAZAKI Shigetoshi; YAMAZAKI Taeko; OGAWA Masao; WATANABE MichiyukiInterfaces or moving boundaries among several phases often arise in many important physical phenomena like bubble motion in fluid, melting ice, crystal growth, and so on. To study such phenomena, numerical simulation is an indispensable tool. We investigated so-called crystalline algorithm, which is one of direct numerical methods for moving boundary problems. We generalized this method and as a result obtained a powerful numerical tool for moving boundary problem. We also solved several related problems. Moreover, we studied their applications.
- 非圧縮性理想流体に対する自由境界問題Date (from‐to) : 1998 -2007渦がある場合の水の波に対する数学解析
- Free boundary problem for an incompressible ideal fluidDate (from‐to) : 1998 -2007Mathematical analysis for water waves with vorticity
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2003 -2005Author : TACHIKAWA Atsushi; OTSUKI Nobukazu; KUBAYASHI Tako; NAGASAWA Takeyuki; OGASAWA MasaoThe aim of this research project is to investigate structures of solutions for geometric variational problems. While we were studying harmonic maps into Finsler manifolds, the necessity of the research on the variational functionals with singularities occurred. So, in this research project, we considered, as important points, regularity of the solutions for variational problems with singularities or weak solutions of partial differential equations with singular coefficients. For this purpose, we investigated partial regularity of minimizers for functionals with VMO (Vanishing Mean Oscillation)-coefficients in cooperation with Prof.Maria Alessandra Ragusa (Universita di Catania (Italy)). As results of cooperation with M.A.Ragusa, we got some results on partial regularity of minimizers. Namely, we proved that if u is a minimizer of certain functional with VMO-coefficients then u satisfies "u is Holder continuous except a subset of the domain whose m-2-ε dimensional Hausdorff measure is 0, where m is the dimension of the domain". On the other hand, each researchers investigated their own problems : T.Nagasawa studied Helfrich variational problem which is one of mathematical models for shape transformation theory of human red blood cells. The existence of associated gradient flow was proved locally for arbitrary initial data, and globally near spheres. M.Ogawa studied free boundary problems for flows of an incompressible ideal fluid. He showed the unique existence of the solution, locally in time, even if the initial surface and the bottom are uneven.