KOBAYASHI TAKAYUKI

Research field (1)： Basic analysis

Research theme for competitive and other funds (29)：

2022 - 2026 Mathematical analysis of the initial value boundary value problem of viscous flows with hyperbolic effects
2018 - 2023 Mathematical analysis of diffusion and diffusion wave property for the solutions to the system of the viscous fluid flow
2016 - 2021 Well-posedness and stability of incompressible and compressible flows with phase transition
2012 - 2017 Free boundary problems for flows with phase transitions consistent with thermodynamics based on maximal regularity theorem
2013 - 2016 Diffusion wave property of the solutions to the system of the viscous fluid flow

2012 - 2016 Analysis of stablity and bifurcation for compressible fluid equations

2010 - 2015 Stability analysis for nonlinear partial differential equations

2010 - 2012 Structure of the solutions to the system ofcompressible fluid

2008 - 2012 Analysis for nonlinear critical phenomena described by mean field equations

2007 - 2009 Asymptotic structure of the solutions to the system of compressible fluid

2007 - 2009 Asymptotic analysis of systems of nonlinear partial differential equations describing motions of viscous fluids

2006 - 2009 Characterization of dissipative structure for partial differential equations and application to the nonlinear stability analysis

2005 - 2006 On a stability of the solutions to the equations of the Compressible flow

2003 - 2006 Study of the stability of solutions to some nonlinear evolution equations based on recent development of real analysis

2003 - 2006 Reseach for the singularities and regularity of solutions to crtical nonlinear partial differential equations

2002 - 2005 Asymptotic behavior of solutions and stability of nonlinear waves for equations of gas motion

2002 - 2004 圧縮性Navier-Stokes方程式の解の漸近安定性の研究

2002 - 2004 A study on asymptotic behavior of solutions for evolution equations

2002 - 2004 Mathematical analysis of thermal convection equations

2002 - 2003 RESEARCH ON GEOMETRIC STRUCTURES OF BANACH AND FUNCTION SPACES AND APPLICATIONS

2001 - 2002 Asymptotic Profiles of Solutions to Nonlinear Convection-Diffusion Equations

1999 - 2002 Asymptotic Analysis for Singularities of Solutions to Nonlinear Partial Differential Equations

2000 - 2001 外部領域における圧縮性Navier-Stokes方程式の解の漸近挙動と拡散の研究

1999 - 2001 Study on the fundamental solutions to the equations of radiating gases and its applications

1999 - 2000 Analysis on Singularities of Solutions to Nonlinear Partial Differential Equations

1999 - 2000 OPERATOR THEORETICAL RESEARCH ON GEOMETRY OF BANACH SPACES AND APPLICATIONS

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

1997 - 1998 Probabilistic and statistical approach to spectra of quantum Hamiltonians.

1995 - 1995 非線形発展方程式の解の構造

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Papers (31)：

T. Kobayashi, M. Murata, H. Saito. Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application. Journal of Mathematical Fluid Mechanics. 2022. 24. 1
T. Kobayashi, M. Misawa, K. Tsuda. Asymptotic Profile for Diffusion Wave Terms of the Compressible Navier-Stokes-Korteweg System. Mathematics. 2021. 9(6). 683. 1-20
T. Kobayashi and M. Murata. The global well-posedness of the compressible fluid model of Korteweg type for the critical case. Differential and Integral Equation. 2021. 34. 5-6. 245-264
T. Kobayashi and K. Tsuda. Time decay estimate with diffusion wave property and smoothing effect for solutions to the compressible Navier-Stokes-Korteweg system. Funkcialaj Ekvacioj. 2021. 64. 163-187
T. Kobayashi and Y. Tsuda. Global existence and time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system under critical condition. Asymptotic Analysis. 2021. 121. 2. 195-217

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MISC (14)：

T. Kobayashi. L2 boundedness of the solutions to the 2D Navier-Stokes equations and hyperbolic Navier-Stokes. RIMS kokyuroku. 2015. 1971. 69-75
T. Kobayashi and T. Suzuki. Weak solutions to the equations of Magnet-Hydrodynamics. Proceedings of the National Institute for Mathematical Science. 2007. 2. 175-180
KOBAYASHI Takayuki, SUZUKI Takashi. Weak Solutions to the Navier-Stokes-Poisson Equations(Mathematical Analysis in Fluid and Gas Dynamics : A conference in honor of Professor Tai-Ping Liu on his 60th Birthday). RIMS Kokyuroku. 2006. 1495. 1-7
小林孝行, 鈴木貴. 星雲方程式の弱解について (波の非線形現象の数理とその応用). 数理解析研究所講究録. 2005. 1430. 76-80
T. Kobayashi, T. Suzuki. Weak solutions to the equations of Magnet-Hydrodynamics. RIMS kokyuroku. 2005. 1430. 76-81

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Books (3)：

応用数理 : 基礎・モデリング・解法
培風館 2015 ISBN:9784563011567
The proceedings on Mathematical Fluid Dynamics and Nonlinear Wave
Gakkōtosho 2015 ISBN:9784762504624
線形代数入門
学術図書出版社 2008 ISBN:9784780601046

Lectures and oral presentations (54)：

On the diffusion wave property for the solutions to the compressible Navier-Stokes -Korteweg system
(Fluids and Maximal Regularit. Kyoto Univ. Japan 2024)
Global well-posedness of the compressible Navier-Stokes-Korteweg system under critical condition
(International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics. Waseda Univ. Japan 2022)
Global existence and time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system under critical condition
("Maximal regularity and nonlinear PDE", RIMS in Kyoto Japan 2019)
Stability problem for a constant equilibrium to the Compressible Navier-Stokes-Korteweg system
("Mathematical Fluid Mechanics and Related Topics", Tokyo Inst. Tech, Tokyo Japan 2018)
Decay property for the Compressible Navier-Stokes-Korteweg system
("Workshop on Mathematical Sciences",Wayamba University, Sri Lanka, 2018)

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Work history (1)：

Association Membership(s) (1)：

日本数学会

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