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## Applicationes Mathematicae

1999 | 26 | 2 | 159-194
Tytuł artykułu

### On global motion of a compressible barotropic viscous fluid with boundary slip condition

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ $ℝ^3$ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the $L_2$-approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to $H^{2+α,1+α/2}(Ω × ℝ_+)$ and the density belongs to $H^{1+α,1/2+α/2}(Ω× ℝ_+)$, α ∈ (1/2,1).
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
159-194
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-07-10
poprawiono
1998-11-12
Twórcy
autor
• Kyushu Institute of Technology, Faculty of Engineering, Interdisciplinary Department, Mathematics, Physics and Information Science, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
• [1] R. A. Adams, Sobolev Spaces, Acad. Press, New York, 1975.
• [2] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian); English transl.: Scripta Series in Mathematics, Winston and Halsted Press, 1979.
• [3] M. Burnat and W. M. Zajączkowski, On local motion of compressible barotropic viscous fluid with the boundary slip condition, to appear.
• [4] K. K. Golovkin, On equivalent norms for fractional spaces, Trudy Mat. Inst. Steklov. 66 (1962), 364-383 (in Russian).
• [5] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1954 (in Russian); English transl.: Pergamon Press, Oxford, 1959; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
• [6] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat conductive fluids, Proc. Japan Acad. Ser. A 55 (1979), 337-342.
• [7] A. Matsumura and T. Nishida, The initial value problems for the equations of motion of compressible viscous and heat conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104.
• [8] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids, Comm. Math. Phys. 89 (1983), 445-464.
• [9] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of general fluids, in: Computing Methods in Applied Sciences and Engineering, V, R. Glowinski and J. L. Lions (eds.), North-Holland, Amsterdam, 1982, 389-406.
• [10] J. Serrin, Mathematical Principles of Classical Fluid Mechanics, Handbuch der Physik, Bd. VIII/1, Springer, Berlin, 1959.
• [11] V. A. Solonnikov and V. E. Shchadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov. 125 (1973), 196-210 (in Russian); English transl.: Proc. Steklov Inst. Math. 125 (1973), 186-199.
• [12] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of a viscous compressible barotropic liquid, Zap. Nauchn. Sem. LOMI 182 (1990), 142-148; also in: Constantin Carathéodory: an International Tribute, M. Rassias (ed.), Vol. 2, World Sci., 1991, 1270-1303.
• [13] G. Ströhmer, About a certain class of parabolic-hyperbolic systems of differential equations, Analysis 9 (1989), 1-39.
• [14] G. Ströhmer, About compressible viscous fluid flow in a bounded domain, Pacific J. Math. 143 (1990), 359-375.
• [15] A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Scuola Norm. Sup. Pisa (4) 10 (1983), 607-647.
• [16] A. Valli and W. M. Zajączkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Comm. Math. Phys. 103 (1986), 259-296.
Typ dokumentu
Bibliografia
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