1998 Fiscal Year Final Research Report Summary
Studies on behaviors of solutions to hydrodynamical equations
| Project/Area Number |
08454031
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 |
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Principal Investigator |
TANIGUCHI Setsuo Kyushu Univ., Grad.Sch.Math., Ass.Prof., 大学院・数理学研究科, 助教授 (70155208)
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| Co-Investigator(Kenkyū-buntansha) |
KAGEI Yoshiyuki Kyushu Univ., Grad, Sch.Math., Ass.Prof., 大学院・数理学研究科, 助教授 (80243913)
SUGITA Hiroshi Kyushu Univ., Grad.Sch.Math.Ass.Prof., 大学院・数理学研究科, 助教授 (50192125)
KAWASHIMA Shuichi Kyushu Univ., Grad.Sch.Math., Prof., 大学院・数理学研究科, 教授 (70144631)
YOSHIKAWA Atsushi Kyushu Univ., Grad.Sch.Math., Prof., 大学院・数理学研究科, 教授 (80001866)
MIYAKAWA Tetsuro Kobe Univ., Dept.Math., Prof., 理学部, 教授 (10033929)
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| Project Period (FY) |
1996 – 1998
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| Keywords | hydrodynamical equation / Navier-Stokes equation / intial value problem / decay order / asymptotic stability / stationary solution / oscillatory integral |
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| Research Abstract |
(1) As for solutions to Navier-Stokes equations, which describe motions of incompressible fluids in unbounded domains, decays at infinity of stationary solutions and time-decays of non-stationary measured in several LP-like norms were studied, and an influence of non- lineality of the equations on the decay was found out. (2) Sufficient conditions for classical and Sobolev type global solutions to Burgers-Helmholtz system were established, and asymptotic behavior of the solutions were obtained. The existence of traveling waves and theire asymptotic stability were seen. (3) A mathematical definition of entropy functions for compressible Euler-Helmholtz system was established. (4) The asymptotic stability of steady flows in infinite layers of viscous incompressible fluids in critical cases of stability has been verified. (5) For the initial value problems associated with Korteweg-de Vires equations, an analytic smoothing effect was found out. (6) A class where one can handle formal asymptotic expansions of solutions to quasilinear positive symmetric systems of hyperbolic equations was introduced, and its basic properties were studied. (7) A new complexification of an abstract Wiener space was proposed. A complex change of variable based on the complexification was established, and appled to study asymptotic behaviors of stochastic oscillatry integrals (methods of stationary phase, saddle point methods, and so on).
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