| Project/Area Number |
09640179
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | KYUSHU UNIVERSITY (1998)
Nagoya University (1997) |
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Principal Investigator |
OGAWA Takayoshi Kyushu University, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (20224107)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Keiichi Science University of Tokyo, Dept.Science, Assit.Prof., 理学部 第一部, 講師 (50224499)
KAWASHITA Mishio Ibaraki University, Dept.Education, Asso.Prof., 教育学部, 助教授 (80214633)
KOZONO Hideo Nagoya University, G.S.of Mathematics, Asso.Prof., 大学院・多元数理科学研究科, 助教授 (00195728)
KAGEI Yoshiyuki Kyushu University, G.S.of Mathematics, Asso.Prof., 大学院・数理学研究科, 助教授 (80243913)
KAWASHIMA Shuuichi Kyushu University, G.S.of Mathematics, Prof., 大学院・数理学研究科, 教授 (70144631)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Nonlinear PDE / Schrodinger equations / dispersive equations / Navier-Stokes equation / compressible fluid mechanics / K-P equation / Oberbeck-Boussinesq equation / Lp theory |
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| Research Abstract |
1. Concerning a system of nonlinear dispersive equations arose from the water wave theory, T.Ogawa discovered a different kind of a smoothing effect mainly due to the special structures of nonlinear coupling and established the local Well-posedness of the solution in a weaker initial data.
2. H.Kozono studied the uniqueness problem for the Leray -Hopff weak solution to the Navier-Stokes equation and showed the uniqueness holds for the critical case, C(O, T ; L^n), suppose that the solution satisfies the small gap condition.
3. M.Kawashita considered unique existence of the strong solutions of the Cauchy prob- lems of the compressible Navier-Stokes equations. These equations are well known as explaining motions of fluid that density may change in time and space variables.
4. K.Kato worked with Dr. P.Pipolo about the solitary wave solutions to general- ized Kadomtsev-Petviashvili equations (KP equations) and proved that solutions are real analytic. Also in a joint work with N.Hayashi and P.Naumkin he studies that there exist scattering states to small initial data for some nonlinear Schr_dinger equations and Hartree equations by using some class of Gevrey functions.
5. S.Kawashima proved the existence and asymptotic stability of shock waves for the simplest model system of a radiating gas. Also, we showed the existence of global solutions to a class of hyperbolic-elliptic coupled systems and obtained the decay estimate of the solutions.
6. Y.Kagei introduced a new approximation to the Oberbeck-Boussinesq equation and showed the existence and uniqueness of solution. Also the stability is discussed.
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