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J-GLOBAL ID：200901030793672700 Update date: Feb. 26, 2025

Shibata Yoshihiro

シバタヨシヒロ | Shibata Yoshihiro

Affiliation and department：
Job title： Professor
Homepage URL (1)： https://www.fluid.sci.waseda.ac.jp/shibata/top.html

Research field (1)： Basic analysis

Research keywords (6)：数値シミュレーション , R-有界作用素 , 変分構造 , 2相問題 , 流体方程式 , Theory of Partial Differential Equations

Research theme for competitive and other funds (33)：

2022 - 2027 非有界領域での2相問題の数学的アプローチと準線形放物型方程式論への拡張
2018 - 2022 Entropy dissipative structure and mathematical analysis for complex fluids
2017 - 2022 Construction of Mathematical Theory of 2 phase fluid flows
2016 - 2019 Modeling of complex fluid phenomena, investigation of multiscale structures and numerical analysis
2013 - 2017 Research of Navier-Stokes equations in undounded domains by real analysis and the energy method

2012 - 2017 Construction of mathematical theory to investigate the macro structure and the mesostructure of the fluid motion

2012 - 2017 流体現象のマクロ構造解明のための解析理論の構築

2011 - 2015 A study on the non-equilibrium statistical mechanics of particle methods based on Hamiltonian mechanics

2009 - 2013 Study on the Navier-Stokes equations on unbounded domains by way of real analysis

2005 - 2009 Establishment of Verified Numerical Computation

2005 - 2008 Research on the Navier-Stokes equations in various unbounded domains by using theory of function spaces

2005 - 2006 The approach of an analytic semigroup for free boundary problems of viscous compressible fluids

2004 - 2006 New development of convective reaction-diffusion systems and validation of numerical computation

2001 - 2004 Research of the Navier-Stokes exterior problem by using dual semigmups and the Lorentz spaces

2001 - 2004 Exterior problem for nonlinear wave equations

1999 - 2001 Theory of hyperloobic systems

1998 - 2000 Stabilization problem for nonlinear wave eq

1997 - 1999 An application of real aualytical wethad to nonlinear evolution eguations

1996 - 1996 Studies on differential equations by microlocal analysis

1995 - 1995 非線形発展方程式の解の構造

1994 - 1994 無限自由度の可積分系に関連した非線形波動現象の解析的研究

1994 - 1994 双曲型方程式の初期値問題

1994 - 1994 接触構造と調和積分

1993 - 1993 非線形発展方程式の解の構造の研究

1992 - 1992 双曲型作用素の研究

1992 - 1992 無限自由度の可積分系に関連した非線波動現象の解析的研究

1991 - 1991 多次元拡散過程及び関連分野の研究

1989 - 1989 函数空間論とそれに関連する解析学と幾何学の研究

流体力学の数理的解析

Real analytic approach to the stability theory of nonlinear evolution equations

Mathematical analysis of interface problems in mathematical physics

Study of the stability of solutions to some nonlinear evolution equations based on recent development of real analysis

Asymptotic behaivours of solutions for nonlinear wave equations

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Papers (147)：

Yoshihiro Shibata, Keiichi Watanabe. Maximal L1-regularity of the Navier-Stokes equations with free boundary conditions via a generalized semigroup theory. Journal of Differential Equations. 2025. 426. 495-605
Thomas Eiter, Mads Kyed, Yoshihiro Shibata. Periodic Lp estimates by R-boundedness: Applications to the Navier-Stokes equations. Acta Applicandae Mathematicae. 2023
Yoshihiro Shibata, Xin Zhang. Global wellposedness of the 3D compressible Navier-Stokes equations with free surface in the maximal regularity class. Nonlinearity. 2023. 36. 7. 3710-3733
Thomas Eiter, Mads Kyed, Yoshihiro Shibata. Falling drop in an ubnouded liquid reservoir:steady-state solutions. Journal of Mathematical Fluid Mechanics. 2023. 25
Hirokazu Saito, Yoshihiro Shibata. On the global wellposedness of free boundary problem for the Navier-Stokes system with surface tension. Journal of Differential Equations. 2023. 384. 1-92

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MISC (7)：

Giovanni P. Galdi, Yoshihiro Shibata. Preface. Lecture Notes in Mathematics. 2020. 2254. v
SHIBATA Yoshihiro, SHIMIZU Senjo. On the Free Boundary Problem for the Navier-Stokes Equations in the $L_p$ Framework and Related Topics (Mathematical Analysis in Fluid and Gas Dynamics). RIMS Kokyuroku. 2009. 1631. 107-120
SHIBATA Yoshihiro, SHIMIZU Senjo. Free boundary problems for a viscous incompressible fluid(Kyoto Conference on the Navier-Stokes Equations and their Applications). RIMS Kokyuroku Bessatsu. 2007. 1. 343-356
Shibata Yoshihiro, Shimizu Senjo. ON THE STOKES EQUATION WITH NEWMANN BOUNDARY CONDITION (Mathematical Analysis in Fluid and Gas Dynamics). RIMS Kokyuroku. 2005. 1425. 40-53
Kubo Takayuki, Shibata Yoshihiro. $L^q-L^r$ estimate of the Stokes semigroup in a perturbed half-space (Harmonic Analysis and Nonlinear Partial Differential Equations). RIMS Kokyuroku. 2004. 1389. 93-119

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Books (6)：

流体数学の基礎上・下
岩波書店 2022
Fluids under pressure
Birkhäuser,Springer 2020 ISBN:9783030396381
Mathematical analysis of the Navier-Stokes equations, Cetraro, Italy 2017
Springer,Fondazione CIME Roberto Conti 2020 ISBN:9783030362256
非線形偏微分方程式
朝倉書店 2012 ISBN:9784254117714
ベクトル解析から流体へ
日本評論社 2007

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Lectures and oral presentations (76)：

R-solver approach to the maximal regularity and free boundary problem for the Navier Stokes equations}
(2023)
R-solver approach to the maximal regularity and free boundary problem for the Navier-Stokes equations
(Birkhauser Distinguished Lecture, https://www.springer.com/journal/21/updates/19753366 2022)
Global well posedness for two phase problem of Navier-Stokes equations in unbounded domains
(International Workshop on Multiphase Flows: Analysis, Modelling and Numerics 2021)
New thought on Matsumura-Nishida theory in the Lp-Lq maximal regularity framework
(Fluid under Control/Summer School 2021 2021)
Matsumura and Nishida theorem in the maximal Lp-Lq regularity framework
(International Workshop on Recent Advances in Nonlinear Partial Differencial Equations 2021)

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Professional career (1)：

理学博士 (筑波大学)

Association Membership(s) (1)：

日本数学会

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