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2016 | OriginalPaper | Chapter

The Work of Yoshihiro Shibata

Authors : Herbert Amann, Yoshikazu Giga, Hisashi Okamoto, Hideo Kozono, Masaso Yamazaki

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

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Abstract

Introducing his research carrier, we address Prof. Yoshihiro Shibata’s great contributions to the mathematical analysis. His out-standing influence to the mathematical society is also clarified.

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next chapter Existence of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows
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Y. Shibata, Lower bounds of solutions of general boundary value problems for differential operators with constant coefficients in a half–space, Japan. J. Math. (N.S.) 8(2), 343–382 (1982)
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75.
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76.
Y. Shibata, On a local existence theorem for quasilinear hyperbolic mixed problems with Neumann type boundary conditions, in Hyperbolic Equations (Padua, 1985) Pitman Research Notes in Mathematics Series, vol. 158 (Longman Scientific & Technical, Harlow, 1987), pp. 282–286
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78.
Y. Shibata, On the Neumann problem for some linear hyperbolic systems of second order. Tsukuba J. Math. 12(1), 149–209 (1988)MathSciNetMATH
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80.
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82.
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Y. Shibata, An exterior initial-boundary value problem for the Navier-Stokes equation, in Nonlinear waves (Sapporo, 1995), GAKUTO International Series Mathematical Sciences Application, vol. 10 (Gakkōtosho, Tokyo, 1997), pp. 431–446
89.
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90.
Y. Shibata, On a Decay Rate of Solutions to One-Dimensional Thermoelastic Equations on a Half Line; Linear Part, ed. by S. Kawashima, T. Yanagisawa. Advances in Nonlinear Partial Differential Equations and Stochastics (World Scientific, Singapore, 1998), pp. 198–291
91.
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92.
Y. Shibata, Global solutions of nonlinear evolution equations and their stability. Sūgaku, 51(1), 1–17 (1999) (in Japanese).MathSciNetMATH
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Y. Shibata, On a stability theorem of the Navier-Stokes equation in a three dimensional exterior domain, in Tosio Kato’s Method and Principle for Evolution Equations in Mathematical Physics, Sapporo, 2001 (1234) (Sūrikaisekikenkyūsho Kōkyūroku, 2001) pp. 146–172
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Y. Shibata, Time-global solutions of nonlinear evolution equations and their stability [translation of Sūgaku 51(1), 1–17 (1999)], in Selected Papers on Analysis and Differential Equations. American Mathematical Society Translations: Series 2, vol. 211 (American Mathematical Society, Providence, RI, 2003), pp. 87–105
97.
Y. Shibata, On some stability theorem of the steady flow of compressible viscous fluid with respect to the initial disturbance, in Hyperbolic Problems and Related Topics, Graduate Series Analysis (International Press, Somerville, MA, 2003), pp. 341–357MATH
98.
Y. Shibata, On the Oseen semigroup with rotating effect. in Functional Analysis and Evolution Equations (Birkhäuser, Basel, 2008), pp. 595–611
99.
Y. Shibata, A stability theorem of the Navier-Stokes flow past a rotating body. in Parabolic and Navier-Stokes Equations. Part 2, vol. 81 (Banach Center Publication, Polish Academy of Science Institute of Mathematics, Warsaw, 2008), pp. 441–455
100.
Y. Shibata, On a C 0 semigroup associated with a modified Oseen equation with rotating effect, in Advances in Mathematical Fluid Mechanics, (Springer, Berlin, 2010), pp. 513–551
101.
Y. Shibata, Generalized resolvent estimates of the Stokes equations with first order boundary condition in a general domain. J. Math. Fluid Mech. 15(1), 1–40 (2013)MathSciNetMATHCrossRef
102.
Y. Shibata, On the \(\mathcal{R}\)-boundedness of solution operators for the weak Dirichlet-Neumann problem, in RIMS Kōkyūroku 1875, Mathematical Analysis of Incompressible Flow (4–6 Feb 2013), ed. by T. Hishida (RIMS, Kyoto University, Kyoto), pp. 1–18
103.
Y. Shibata, On the \(\mathcal{R}\)-boundedness of solution operators for the Stokes equations with free boundary condition. Differ. Integr. Equ. 27(3–4), 313–368 (2014)MathSciNetMATH
104.
Y. Shibata, On some free boundary problem of the Navier-Stokes equations in the maximal L p -L q regularity class. J. Differ. Equ. 258, 4127–4155 (2015)MathSciNetMATHCrossRef
105.
Y. Shibata, On the global well-posedness of some free boundary problem for a compressible barotropic viscous fluid flow, in The Contemporary Mathematics Series of the American Mathematical Society: Recent Advances in PDEs and Applications, Levico Terme, 17–21 February 2014 [to celebrate the 70th Birthday of Professor Hugo Beirao da Veiga]
106.
Y. Shibata, Local well-posedness of compressible-incompressible two-phase flows with phase transitions, To appear in the Proceedings of Levico Conf. on fluid Dyn and Electromagnetism. arXiv:submit/1156284 [math. AP] 10 Jan 2015
107.
Y. Shibata, On the \(\mathcal{R}\)-boundedness for the two phase problem with phase transition: compressible-incompressible model problem. Funk. Ekvaj. (to appear)
108.
Y. Shibata, W. Dan, On a local energy decay of solutions of a dissipative wave equation, inMathematical Analysis of Phenomena in Fluid and Plasma Dynamics (Japanese) (862) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 1993/1994) pp. 181–190
109.
Y. Shibata, S. Mu Zheng, On some nonlinear hyperbolic system with damping boundary condition. Nonlinear Anal. TMA 17(3), 233–266 (1991)MathSciNetMATHCrossRef
110.
Y. Shibata, Y. Tsutsumi, Global existence theorem for nonlinear wave equations in exterior domain, in Recent Topics in Nonlinear PDE (Hiroshima, 1983), North-Holland Mathematics Studies vol. 98 (North-Holland, Amsterdam, 1984) pp. 155–196
111.
Y. Shibata, Y. Tsutsumi, Global existence theorem for nonlinear wave equation in exterior domain. Proc. Japan Acad. A Mat. Sci. 60(1), 14–17 (1984)MathSciNetMATHCrossRef
112.
Y. Shibata, Y. Tsutsumi, Local existence of \(C^{\infty }\)–solution for the initial–boundary value problem of fully nonlinear wave equation. Proc. Japan Acad. Ser. A Math. Sci. 60(5), 149–152 (1984)MathSciNetMATHCrossRef
113.
Y. Shibata, Y. Tsutsumi, On a global existence theorem of Neumann problem for some quasilinear hyperbolic equations, in Recent Topics in Nonlinear PDE, II (Sendai, 1984), North-Holland Mathematics Studies, vol. 128 (North-Holland, Amsterdam, 1985), pp. 175–228
114.
Y. Shibata, Y. Tsutsumi, On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain. Math. Z. 191(2), 165–199 (1986)MathSciNetMATHCrossRef
115.
Y. Shibata, Y. Tsutsumi, Local existence of solutions for the initial boundary value problem of fully nonlinear wave equation. Nonlinear Anal. TMA 11(3), 335–365 (1987)MathSciNetMATHCrossRef
116.
Y. Shibata, S.Shimizu, A decay property of the Fourier transform and its application to the Stokes problem. J. Math. Fluid Mech. 3(3), 213–230 (2001)MathSciNetMATHCrossRef
117.
Y. Shibata, S. Shimizu, On a resolvent estimate of the interface problem for the Stokes system in a bounded domain, Harmonic Analysis and Nonlinear Partial Differential Equations (Japanese) (1235) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 2001), pp. 132–159MATH
118.
Y. Shibata, S. Shimizu, On the L p and Schauder estimates of solutions to elastostatic interface problems, in Proceedings of the Fourth International Conference on Functional Analysis and Approximation Theory, Potenza, 2000, vol. II; Rend. Circ. Mat. Palermo (2) Suppl. 68(Part II), 821–835 (2002)
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P. Secchi, Y. Shibata, On the decay of solutions to the 2D Neumann exterior problem for the wave equation. J. Differ. Equ. 194(1), 221–236 (2003)MathSciNetMATHCrossRef
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Y. Shibata, S. Shimizu, On a resolvent estimate for the Stokes system with Neumann boundary condition. Differ. Integr. Equ. 16(4), 385–426 (2003)MathSciNetMATH
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Y. Shibata, S. Shimizu, Applications of the Fourier transform to some resolvent estimates for the Stokes system, in Progress in Analysis, vols. I, II (Berlin, 2001) (World Science Publisher, River Edge, 2003), pp. 125–134
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Y. Shibata, S. Shimizu, L p –L q maximal regularity and viscous incompressible flows with free surface. Proc. Japan Acad. Ser A, Math. Sci. 81(9), 151–155 (2005)
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Y. Shibata, S. Shimizu, On the stokes equation with neumann boundary condition, in Regularity and other Aspects of the Navier-Stokes Equations. Banach Center Publication, vol. 70 (Polish Academy of Sciences, Warsaw, 2005), pp. 239–250
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Y. Shibata, S. Shimizu, On a Free Boundary Problem for the Navier-Stokes Equations. Differ. Integr. Equ. 20(3), 241–276 (2007)MathSciNetMATH
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Y. Shibata, S. Shimizu, L p -L q regularity for the two-phase Stokes equations; model problems. J. Differ. Equ. 251(2), 373–419 (2011)MathSciNetMATHCrossRef
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Y. Shibata, S. Shimizu, On the maximal L p -L q regularity of the Stokes problem with first order boundary condition; model problems, J. Math. Soc. Jpn. 64(2), 561–626 (2012)MathSciNetMATHCrossRef
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Y. Shibata, M. Yamazaki, On some stability theorem of the Navier-Stokes equation in the three dimensional exterior domain, in Mathematical Analysis of Liquids and Gases (Japanese) (Kyoto, 1999) (1146) (Sūrikaisekikenkyūsho Kōkyūroku, 2000), pp. 73–91
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K. Tanaka, Y. Shibata, On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance. J. Math. Soc. Jpn. 55(3), 797–826 (2003)MathSciNetMATHCrossRef
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T. Hishida, Y. Shibata, Decay estimates of the Stokes flow around a rotating obstacle, in Kyoto Conference on the Navier-Stokes Equations and Their Applications. RIMS Kokyūroku Bessatsu, vol. B1 pp. 167–186 (Res. Inst. Math. Sci. (RIMS), Kyoto, 2007)
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Y. Shibata, S. Shimizu, Free boundary problems for a viscous incompressible fluid, in Kyoto Conference on the Navier-Stokes Equations and Their Applications. RIMS Kokyūroku Bessatsu, vol. B1 (Res. Inst. Math. Sci. (RIMS), Kyoto, 2007), pp. 343–358
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Y. Shibata, S. Shimizu, On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations. Mathematische Nachrichten 282(3), 482–499 (2009)MathSciNetMATHCrossRef
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Y. Shibata, K. Tanaka, Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid. Comput. Math. Appl. 53(3–4), 605–623 (2007)MathSciNetMATHCrossRef
Metadata
Title
The Work of Yoshihiro Shibata
Authors
Herbert Amann
Yoshikazu Giga
Hisashi Okamoto
Hideo Kozono
Masaso Yamazaki
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_1

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