Details of a Researcher

Soga Kohei

写真a

Affiliation: Faculty of Science and Technology, Department of Mathematics （Yagami）

Position: Associate Professor

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Papers 【 Display / hide 】

Existence of global weak solutions of inhomogeneous incompressible Navier–Stokes system with mass diffusion

Kacedan E., Soga K.

Zeitschrift fur Angewandte Mathematik und Physik （Zeitschrift fur Angewandte Mathematik und Physik) 75 （ 2 ） 2024.04

ISSN 00442275

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This paper proves existence of a global weak solution to the inhomogeneous (i.e., non-constant density) incompressible Navier–Stokes system with mass diffusion. The system is well-known as the Kazhikhov–Smagulov model. The major novelty of the paper is to deal with the Kazhikhov–Smagulov model possessing the non-constant viscosity without any simplification of higher order nonlinearity. Every global weak solution is shown to have a long time behavior that is consistent with mixing phenomena of miscible fluids. The results also contain a new compactness method of Aubin–Lions–Simon type.
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Mathematical analysis of modified level-set equations

Bothe D., Fricke M., Soga K.

Mathematische Annalen （Mathematische Annalen) 2024

ISSN 00255831

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The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation by introducing a nonlinear term to preserve certain geometrical features of the level-set function, where the zero level-set must stay invariant under the modification. The present work establishes mathematical justification for a specific class of modified level-set equations on a bounded domain, generated by a given smooth velocity field in the framework of the initial/boundary value problem of Hamilton–Jacobi equations. The first main result is the existence of smooth solutions defined in a time-global tubular neighborhood of the zero level-set, where an infinite iteration of the method of characteristics within a fixed small time interval is demonstrated; the smooth solution is shown to possess the desired geometrical feature. The second main result is the existence of time-global viscosity solutions defined in the whole domain, where standard Perron’s method and the comparison principle are exploited. In the first and second main results, the zero level-set is shown to be identical with the original one. The third main result is that the viscosity solution coincides with the local-in-space smooth solution in a time-global tubular neighborhood of the zero level-set, where a new aspect of localized doubling the number of variables is utilized.
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A Remark on Tonelli’s Calculus of Variations

Soga K.

Russian Journal of Nonlinear Dynamics （Russian Journal of Nonlinear Dynamics) 19 （ 2 ） 239 - 248 2023

ISSN 26585324

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This paper provides a quite simple method of Tonelli’s calculus of variations with positive definite and superlinear Lagrangians. The result complements the classical literature of calculus of variations before Tonelli’s modern approach. Inspired by Euler’s spirit, the proposed method employs finite-dimensional approximation of the exact action functional, whose minimizer is easily found as a solution of Euler’s discretization of the exact Euler – Lagrange equation. The Euler – Cauchy polygonal line generated by the approximate minimizer converges to an exact smooth minimizing curve. This framework yields an elementary proof of the existence and regularity of minimizers within the family of smooth curves and hence, with a minor additional step, within the family of Lipschitz curves, without using modern functional analysis on absolutely continuous curves and lower semicontinuity of action functionals.
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Mathematical Analysis of Finite Difference Method Applied to Hamilton-Jacobi Equations: A Stochastic and Variational Approach

Kohei Soga

学会誌「応用数理」（日本応用数理学会) 32 （ 3 ） 127 - 138 2022.09

Research paper (scientific journal), Single Work, Lead author, Accepted
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More on Convergence of Chorin’s Projection Method for Incompressible Navier–Stokes Equations

Maeda M., Soga K.

Journal of Mathematical Fluid Mechanics （Journal of Mathematical Fluid Mechanics) 24 （ 2 ） 2022.05

ISSN 14226928

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Kuroki–Soga (Numer. Math. 146:401–433, 2020) proved that Chorin’s fully discrete finite difference projection method, originally introduced by Chorin (Math. Comput. 23:341–353, 1969), is unconditionally solvable and convergent within an arbitrary fixed time interval to a Leray–Hopf weak solution of the incompressible Navier–Stokes equations on a bounded domain with an arbitrary external force. This paper is a continuation of Kuroki–Soga’s work to further exhibit mathematical aspects of the method. We show time-global solvability and convergence of the scheme; L2-error estimates for the scheme in the class of smooth exact solutions; application of the method to the problem with a time-periodic external force to investigate time-periodic (Leray–Hopf weak) solutions, long-time behaviors, error estimates, etc.
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Papers, etc., Registered in KOARA 【 Display / hide 】

Mathematical analysis of numerical methods in fluid dynamics

Soga, Kohei

福澤諭吉記念慶應義塾学事振興基金事業報告集（福澤基金運営委員会) 2022
Applied analysis for nonlinear problems

Soga, Kōhei

科学研究費補助金研究成果報告書 2018

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Presentations 【 Display / hide 】

A Finite Difference Method in Hamilton-Jacobi Equations and Weak KAM Theory

Kohei Soga

12th AIMS Conference in Taipei (Taiwan ) ,

2018.07
,
Oral presentation (invited, special)
On convergence of Chorin's projection method to a Leray-Hopf weak solution -Bounded Lipschitz domain case-

Kohei Soga

Conference on Mathematical Fluid Dynamics Bad Boll (Germany) ,

2018.05
,
Oral presentation (invited, special)
ハミルトン・ヤコビ方程式のディスカウント近似に対する選択問題：収束率

SOGA KOHEI

日本数学会２０１７年度年会 (首都大学東京) ,

2017.03
,
Oral presentation (general)
弱KAM理論の応用１　ーHJ方程式の放物型近似・差分近似・discount近似と対応する力学系

SOGA KOHEI

RIMS研究集会: 力学系とその関連分野の連携探索 (京都大学) ,

2016.06
,
Oral presentation (invited, special)
古典KAM理論・弱KAM理論入門

SOGA KOHEI

RIMS研究集会: 力学系とその関連分野の連携探索 (京都大学) ,

2016.06
,
Oral presentation (invited, special)

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

流体力学における数値解法の数学解析と解析力学における古典KAM理論の数学解析

2022.04

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2027.03

MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(C), Principal investigator
力学系・流体力学の応用解析的研究

2018.04

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2022.03

MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Early-Career Scientists , Principal investigator
応用解析としての非線形問題の研究

2015.04

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2019.03

MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Principal investigator