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Real analytic approach to the stability theory of nonlinear evolution equations

Research Project

Project/Area Number 12440045
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionWaseda University

Principal Investigator

SHIBATA Yoshihiro  Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (50114088)

Co-Investigator(Kenkyū-buntansha) YAMAZAKI Masao  Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (20174659)
KAJI Hajime  Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (70194727)
TANAKA Kazunaga  Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (20188288)
KOBAYASHI Takayuki  Saga University, The department of Sciences, Assistant Professor, 理学部, 助教授 (50272133)
SHIMIZU Senjo  Shizuoka University, The department of Engineering, Assistant Professor, 工学部, 助教授 (50273165)
Project Period (FY) 2000 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥14,600,000 (Direct Cost: ¥14,600,000)
Fiscal Year 2003: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2002: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2001: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥3,800,000 (Direct Cost: ¥3,800,000)
KeywordsOseen equation / Flew in the infinite layer / Stokes operator / Stability of the flew / Resolvent problem / Incompressible viscous fluid flow / Compressible viscous fluid flow / Free boundary value problem / 数学 / 基礎解析 / n-dim. Navier-Stokes equation / Stability / Ossen equation / Compressible fluid / 2 phase problem for the Stokes eq. / Ginzuburg-Landau-Maxwell eq. / Perfect wall conditon / Stokes eq. in the half space / Infinite layer domain / Ginzburg-Landau方程式 / 定常解の安定性 / Perfect wall condition / Stokes方程式 / オゼン方程式 / ストークス方程式 / 弾性体の方程式 / 2相問題 / 安定性 / 重み付き評価
Research Abstract

1.Stability of the Oseen flow in the n-dimensional exterior domain (n>2).
2.Stability of the Couette flow and the Poiseuille flow in the infinite layer.
3.Rate of convergence of the non-stationary flow to the stationary flow of compressible viscous fluid.
4.Resolvent estimate of solutions to the Stokes equation with Neumann boundary condition.

Report

(5 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (41 results)

All Other

All Publications (41 results)

  • [Publications] V.Enomoto, Y.Shibata: "Local energy decay of solutions to the Oseen equation in the exterior domains"Indiana Univ.Math.J.. (印刷中). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Abe, Y.Shibata: "On a generalized resolvent estimate of the Stokes equation on an infinite layer, Part 1"J.Math.Soc.Japan. 55. 469-497 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, K.Tanaka: "On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance"J.Math.Soc.Japan. 55. 797-826 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, S.Shimizu: "On some resolvent estimates for the Stokes system with Neumann boundary condition"Diff.Int.Eqns.. 16. 385-426 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] V.Shibata, S.Shimizu: "On a resolvent estimate of the literface problem for the Stokes system in a bounded domain"J.Diff.Eqns.. 191. 408-444 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] P.Secchi, Y.Shibata: "On the decay of solutions to the 2D Neumann exterior problem for the wave equation"J.Diff.Eqns.. 194. 408-444 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Enomoto, Y.Shibata: "Local energy decay of solutions to the Oseen equation in the exterior domain"Indiana Univ. Math. J. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Abe, Y.Shibata: "On a generalized resolvent estimate of the Stokes equation on an infinite layer, Part 1"J. Math. Soc. Japan. 55. 469-497 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, K.Tanaka: "On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance"J. Math. Soc. Japan. 55. 797-826 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, S.Shimizu: "On some resolvent estimates for the Stokes system with Neumann boundary condition"Diff. Int. Eqns.. 16. 385-426 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, S.Shimizu: "On a resolvent estimate of the interface problem for the Stokes system in abouded domain"J. Diff. Eqns.. 191. 408-444 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Secchi, Y.Shibata: "On the decay of solutions to the 2D Neumann exterior problem for the wave equation"J. Diff. Eqns.. 194. 221-236 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Abe, Y.Shibata: "On a generalized resolvent estimate of the Stokes equation on an infinite layer, Part 2"J. Math. Fluid. Mech.. 5. 245-274 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Kobayashi, Y.Shibata: "Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations"Pacific J. Math.. 207. 199-234 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, S.Shimizu: "A decay property of the Fourier transform and its application to the Stokes problem"J. Math. Fluid Mech.. 3. 213-230 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata: "On the rate of decay of solutions to linear viscoelastic equation"Math. Meth. Appl. Sci.. 23. 203-226 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Shibata, S.Shimizu: "On a resolvent estimate for the Stokes systme with Neumann boundary condition"Differential and Integral Equations. 16. 385-426 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Shibata, S.Shimizu: "On a resolvent estimate of the interface problem for the Stokes system in a bounded domain"Journal of Differential Equations. 191. 408-444 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] P.Secchi, Y.Shibata: "On the decay of solutions to the 2D Neumann exterior problem for the wave equation"Journal of Differential Equations. 194. 221-236 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Abe, Y.Shibata: "On a resolvent estimate of the Stokes equation on an infinite layer"Journal of Mathematical Society of Japan. 55. 469-497 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Abe, Y.Shibata: "On a resolvent estimate of the Stokes equation on an infinite layer, Part 2"Journal of Mathematical Fluid Mechanics. 5. 245-274 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Shibata, K.Tanaka: "On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance"Journal of Mathematical Society of Japan. 55. 797-826 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Shibata: "Time-global solutions of nonlinear evolution equations and their stability"American Mathematical Society, Translations. 211. 87-105 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 小林孝行, 柴田良弘: "Remark on the rate of decay of solutions to linearlized compressible Navier-Stokes equations"Pacific Journal of Mathematics. 207巻1号. 199-234 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 小林孝行: "Some estimates of solutions for the equations of motion of compressible viscous fluid in an exterior domain in R^3"Journal of Differential Equations. 184巻. 587-561 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 柴田良弘, 清水扇丈: "On the L_p and Schauder Estimates of Solutions to Elastostatic Interface Problems"Supplemento di rendiconti del Circolo matematico di Palermo. 68巻. 821-835 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 柴田良弘, 清水扇丈: "On some resolvent estimates for the Stokes system"Differential and Integral Equation. (発表予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 柴田良弘, 清水扇丈: "On a resolvent estimate of the interface problem for the Stokes system in a bounded domain"Journal of Differential Equations. (発表予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 柴田良弘, 田中孝明: "On the steady flow of compressible viscous fluid and its stability with Respect to initial disturbance"Journal of Mathematical Society of Japan. (発表予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 柴田 良弘, 清水 扇丈: "A decay property of the Fourier image and its application to Stokes problem"J. Math. Fluid Mech.. 3巻・3号. 213-230 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 柴田 良弘, 清水 扇丈: "On the L^p and Schauder Estimates of Solutions to Elastostaic Interface Problem"Remd. Circ. Mat. Palermo. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 小林 孝行, 柴田 良弘: "Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations"Pacific J. Math. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 小林 孝行: "Some estimate s of solutions for the equations of motion of compressible viscous fluid in an exterior domain in R^3"J. Differenctial Equations. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 小林 孝行: "L_2 and L_W estimates of the solutions for the compressible Navier-Stokes equations in a 3D exterior domain"Publ. RIMS. Kyoto Univ.. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 山崎 昌男: "The Navier-Stokes Equation in Various Function Spaces"AMS Transrations Series 2. 204巻. 111-132 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 山崎昌男: "The Navier-Stokes equations in the weak Ln space with time-dependent external force"Math.Ann.. 317. 635-675 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 山崎昌男: "Solutions in the Morrey spaces of the Navier-Stokes equation with time-dependent external force"Funkcialaj Ekvacioj. 43. 419-460 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 小林孝行: "Some estimates of solutions for the equation of compressible viscous fluid in a 3D exterior domain"Progress in Nonlinear Diff.Eqns and Their Applications. 42. 151-158 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 清水扇丈: "Singularities of the reflected and refracted Riemann functions of elastic wave propagation problems in stratified media"Int.Soc.Anal.Comput.. 5. 343-362 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 清水扇丈: "Inner estimate of singularities to solutions for elastic wave propagation problems in stratified media"Commun.Math.Phys.. 208. 541-574 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 柴田良弘,清水扇丈: "A decay property of the Fourier image and its application to the Stokes problem"J.Math.Fluid.Mech.. 3(発表予定). (2001)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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