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Tytuł książki

On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

Autorzy

Wojciech M. Zajączkowski

Seria

Rozprawy Matematyczne tom/nr w serii: 324 wydano: 1993

Zawartość

Pełne teksty: http://matwbn.icm.edu.pl/ksiazki/rm/rm324/rm32401.pdf [zdalny]

Warianty tytułu

Abstrakty

EN
We consider the motion of a viscous compressible barotropic fluid in $ℝ^3$ bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.

CONTENTS
1. Introduction.......................................5
2. Global estimates and relations........11
3. Local existence...............................16
4. Global differential inequality............44
5. Korn inequality................................81
6. Global existence.............................89
References.......................................100

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 324

Liczba stron

101

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCXXIV

Daty

wydano
1993
otrzymano
1991-07-03
poprawiono
1992-01-28
poprawiono
1992-08-31

Twórcy

autor
Wojciech M. Zajączkowski
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York 1975.
  • [2] G. Allain, Small-time existence for the Navier-Stokes equations with a free surface, Appl. Math. Optim. 16 (1987), 37-50.
  • [3] J. T. Beale, The initial value problem for the Navier-Stokes equations with a free boundary, Comm. Pure Appl. Math. 31 (1980), 359-392.
  • [4] J. T. Beale, Large time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-352.
  • [5] 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.
  • [6] O. A. Ladyzhenskaya and V. A. Solonnikov, On some problems of vector analysis and generalized formulations of boundary problems for Navier-Stokes equations, Zap. Nauchn. Sem. LOMI 59 (1976), 81-116 (in Russian).
  • [7] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow 1984 (in Russian); English transl.: Pergamon Press, Oxford 1959; new edition: Hydrodynamics, Nauka, Moscow 1986 (in Russian).
  • [8] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104.
  • [9] 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.
  • [10] A. Matsumura and T. Nishida, The initial boundary value problem for the equations of motion of compressible viscous and heat-conductive fluid, preprint of Univ. of Wisconsin, MRC Technical Summary Report no. 2237 (1981).
  • [11] 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, R. Glowinski and J. L. Lions (eds.), North-Holland, Amsterdam 1982, 389-406.
  • [12] 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.
  • [13] S. M. Nikol'skiĭ, Approximation of Functions of Several Variables and Imbedding Theorems, Nauka, Moscow 1977 (in Russian).
  • [14] T. Nishida, Equations of fluid dynamics : free surface problems, Comm. Pure Appl. Math. 39 (1986), 221-238.
  • [15] K. Pileckas and W. M. Zajączkowski, On free boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 129 (1990), 169-204.
  • [16] P. Secchi, On the uniqueness of motion of viscous gaseous stars, Math. Methods Appl. Sci. 13 (1990), 391-404.
  • [17] P. Secchi, On the motion of gaseous stars in the presence of radiation, Comm. Partial Differential Equations 15 (1990), 185-204.
  • [18] P. Secchi, On the evolution equations of viscous gaseous stars, Ann. Scuola Norm. Sup. Pisa (2) 18 (1991), 295-318.
  • [19] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids, J. Reine Angew. Math. 341 (1983), 1-31.
  • [20] V. A. Solonnikov, Free boundary problems and problems in noncompact domains for the Navier-Stokes equations, in: Proc. Internat. Congress Math. Berkeley, California 1986 (1987), 1113-1122.
  • [21] V. A. Solonnikov, On an initial-boundary value problem for the Stokes system which appears in free boundary problems, Trudy Mat. Inst. Steklov. 188 (1990), 150-188 (in Russian).
  • [22] V. A. Solonnikov, On the solvability of the initial-boundary value problem for equations of motion of the viscous compressible fluid, Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (in Russian).
  • [23] V. A. Solonnikov, On an unsteady flow of a finite mass of a liquid bounded by a free surface, Zap. Nauchn. Sem. LOMI 152 (1986), 137-157 (in Russian); English transl.: J. Soviet Math. 40 (4) (1988), 672-686.
  • [24] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967).
  • [25] V. A. Solonnikov, Solvability of the evolution problem for an isolated mass of a viscous incompressible capillary liquid, Zap. Nauchn. Sem. LOMI 140 (1984), 179-186 (in Russian); English transl.: J. Soviet Math. 32 (2) (1986), 223-238.
  • [26] V. A. Solonnikov, On an unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (5) (1987), 1065-1087 (in Russian).
  • [27] V. A. Solonnikov, Solvability of a problem on the motion of a viscous incompressible fluid bounded by a free surface, Izv. Akad. Nauk SSSR Ser. Mat. 41 (6) (1977), 1388-1424 (in Russian); English transl.: Math. USSR-Izv. 11 (6) (1977), 1323-1358.
  • [28] V. A. Solonnikov, Estimates of solutions of an initial-boundary value problem for the linear nonstationary Navier-Stokes system, Zap. Nauchn. Sem. LOMI 59 (1976), 178-254 (in Russian); English transl.: J. Soviet Math. 10 (2) (1978), 336-393.
  • [29] V. A. Solonnikov, On the solvability of the second initial-boundary value problem for the linear nonstationary Navier-Stokes system, Zap. Nauchn. Sem. LOMI 69 (1977), 200-218 (in Russian); English transl.: J. Soviet Math. 10 (1) (1978), 141-193.
  • [30] V. A. Solonnikov, A priori estimates for second order parabolic equations, Trudy Mat. Inst. Steklov. 70 (1964), 133-212 (in Russian).
  • [31] V. A. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with surface tension, in: Constantine Carathéodory: An International Tribute, T. M. Rassias (ed.), World Scientific, 1991, 1270-1303.
  • [32] 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.
  • [33] 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.
  • [34] W. M. Zajączkowski, On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations, Dissertationes Math. 304 (1990).
  • [35] W. M. Zajączkowski, On nonstationary motion of a compressible viscous capillary fluid bounded by a free surface, to appear.
  • [36] W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid bounded by a free surface, in: Partial Differential Equations, Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., Warszawa 1992, 511-553.
  • [37] W. M. Zajączkowski, Local existence of solutions for free boundary problems for viscous fluids, to appear.

Języki publikacji

EN

Uwagi

1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.

Identyfikator YADDA

bwmeta1.element.zamlynska-a47e081b-3af2-4f6b-bdd3-d756024211c4

Identyfikatory

ISBN
83-85116-81-8
ISSN
0012-3862

Kolekcja

DML-PL
Zawartość książki

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