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Studies on behaviors of solutions to hydrodynamical equations

Research Project

Project/Area Number 08454031
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

TANIGUCHI Setsuo (1997-1998)  Kyushu Univ., Grad.Sch.Math., Ass.Prof., 大学院・数理学研究科, 助教授 (70155208)

宮川 鉄朗 (1996)  九州大学, 大学院・数理学研究科, 教授 (10033929)

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)
濱名 裕治  九州大学, 大学院・数理学研究科, 助教授 (00243923)
谷口 説男  九州大学, 大学院・数理学研究科, 助教授 (70155208)
国田 寛  九州大学, 大学院・数理学研究科, 教授 (30022552)
Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordshydrodynamical equation / Navier-Stokes equation / intial value problem / decay order / asymptotic stability / stationary solution / oscillatory integral / 漱近解析 / 非線形方程式 / ナビア=ストークス / 漸近挙動 / 弱解 / 減衰オーダー / 非圧縮粘性流体 / 圧縮粘性流体 / 衝撃波 / 膨張波 / 安定性 / 分岐
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).

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] P.Malliavin.S.Taniguchi: "Analytic functions,Cauchy formula,and statinary phase on a real abstract Wiener space" Jour.Funct.Anal.143. 470-528 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita,S.Taniguchi: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" Jour.Funct.Anal.155. 229-262 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Miyakawa: "Hardy spaces of solenoidal vector fields,with applications to the Navier-Stokes equations," Kyushu Journal of Mathematics. 50. 1-64 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Miyakawa: "Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in R^n" Funkcialaj Ekvacioj. 41. 383-434 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Hattori,S.Kawashima: "Nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory" Jour.Differential Equations. 127. 174-196 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] W.von Wahl,Y.Kagei: "Asymptotic stability of steady flows in infinite layers of viscous incompressible fluids in critical cases of stability" Indiana Univ.Math.Jour.印刷中.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] P.Malliavin, S.Taniguchi: "Analytic functions, Cauchy formula, and statinary phase on a real abstract Wiener Space" Jour.Funct.Anal.143. 470-528 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Suhita, S.Taniguchi: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" Jour.Funct.Anal.155. 229-262 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Miyakawa: "Hardy spaces of solenoidal vector fields, with applications to the Navier-Stokes equations" Kyushu Journal of Mathe-matics. 50. 1-64 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Miyakawa: "Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in R^n" Funkcialaj Ekvacioj. 41. 383-434 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Hattori, S.Kawashima: "Nonlinear stability of travel-ling wave solutions for viscoelastic materials with fad-ing memory" Jour.Differential Equa-tions. 127. 174-196 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] W.von Wahl, Y.Kagei: "Asymptotic stability of steady flows in infinite layers of viscous incompressible fluids in critical cases of stability" Indiana Univ.Math.Jour.(in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Miyakawa: "Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in R^n" Funkcialaj Ekvacioj. 41. 383-434 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Yoshikawa: "Modulation Equations for planar phases and asymptotic weak solutions" Kyushu Journal of Mathemathics. 52. 99-148 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita,S.Taniguchi: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" Journal of Functional Analysis. 155. 229-262 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] W.von Wahl,Y.Kagei: "Asymptotic stabillity of steady flowsin infinite layers of viscous incompressible fluids in critical cases of stabillity," Indiana Univ.Math.Jour.(印刷中).

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Taniguchi: "Stochastic oscillatory integrals with quadratic phase fupction and Jacobi equations" Probabilty Theory and Related Fields. (掲載予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Tetsuro Miyakawa: "On L^1-stability of stationary Navier-Stokes flows in IR^n" Journal of Mathematical Science Univ.Tokyo. 4・1. 67-119 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tetsuro Miyakawa: "Decay properties of weak solutions to a perturbed Navier-Stokes system in IR^n" Advances in Mathematical Sciences and Applications. 7・2. 741-770 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Setsuo Taniguchi: "Analytic functions,Cauchy formula,and stationary Phase on a real abstract Wiener spac" Journal of Functional Analysis. 143・2. 470-528 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Setsno Taniguchi: "On the exponential decay of oscillatory integrals on an abstract Wiener space" Journal of Functional Analysis. 153. 印刷中 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Sugita: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" Journal of Functional Analysis. 154. 印刷中 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Yuji Hamana: "The fluctuation result for the multiple point range of two dincelrsional recurrent random walles" Annals of Probabilify. 25. 598-639 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Zhi-Min Chen: "Decay properties of weak solutions to a perturbed Navier-Stokes system in R^n." Advances in Math.Sci.and Appl.(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] Tetsuro Miyakawa: "On L^1 stability of stationary Navier-Stokes flows in R^n." Journal of Math.Sci.,Univ.of Tokyo. (発表予定).

    • Related Report
      1996 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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