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Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow

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Contributions to Current Challenges in Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

Steady compressible Navier-Stokes equations with zero velocity conditions at infinity are studied in a three-dimensional exterior domain. The case of small perturbations of large potential forces is considered. In order to solve the problem, a decomposition scheme is applied and the nonlinear problem is decomposed into three linear problems: Neumann-type problem, modified Stokes problem and transport equation. These linear problems are solved in weighted function spaces with detached asymptotics. The results on existence, uniqueness and asymptotics for the linearized problem and for the nonlinear problem are proved.

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References

  1. W. Borchers and K. Pileckas. Existence, uniqueness and asymptotics of steady jets. Arch. Rat. Mech. Analysis 120 (1983), 1–49.

    Article  MathSciNet  ADS  Google Scholar 

  2. A. Matsumura and T. Nishida. Initial boundary value problems for equations of motion of compressible viscous and heat-conductive fluids. Comm. Math. Phys. 89 (1983), 445–464.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. S.A. Nazarov. On the two-dimensional aperture problem for Navier-Stokes equations. C.R. Acad. Sci. Paris, Ser. 1 323 (1996), 699–703.

    Google Scholar 

  4. S.A. Nazarov. The Navier-Stokes problem in a two-dimensional domains with angular outlets to infinity. Zapiski Nauchn. Seminarov POMI 257 (1999), 207–227 (in Russian).

    Google Scholar 

  5. S.A. Nazarov. Weighted spaces with detached asymptotics in application to the Navier-Stokes equations. Advances in Math. Fluid Mechanics, Lecture Notes of the Sixth International School “Mathematical Theory in Fluid Mechanics”, J. Malek, J. Necas, M. Rokyta (Eds.), Springer, 2000, 159–191.

    Google Scholar 

  6. S.A. Nazarov and K. Pileckas. On steady Stokes and Navier-Stokes problems with zero velocity at infinity in a three-dimensional exterior domain. J. Math. Kyoto Univ. 40(3) (2000), 475–492.

    MathSciNet  MATH  Google Scholar 

  7. S.A. Nazarov and K. Pileckas. Asymptotics of solutions to the Navier-Stokes equations in the exterior of a bounded body. Doklady RAN 367(4) (1999), 461–463. English transl.: Doklady Math. 60(1) (1999), 133–135.

    MathSciNet  Google Scholar 

  8. S.A. Nazarov and K. Pileckas. Asymptotic conditions at infinity for the Stokes and Navier—Stokes problems in domains with cylindrical outlets to infinity. Advances in Fluid Dynamics, Quaderni di Matematica, P. Maremonti (Ed.) 4 (1999), 141–243.

    Google Scholar 

  9. S.A. Nazarov and B.A. Plamenevskii. Elliptic boundary value problems in domains with piecewise smooth boundaries. Walter de Gruyter and Co, Berlin, 1994.

    Book  Google Scholar 

  10. S.A. Nazarov, A. Sequeira and J.H. Videman. Asymptotic behaviour at infinity of three-dimensional steady viscoelastic flows. Pacific J. Math. 203 (2002), 461–488.

    Article  MathSciNet  MATH  Google Scholar 

  11. S.A. Nazarov, M. Specovius-Nengebaner and G. Thäter. Quiet flows for Stokes and Navier—Stokes problems in domains with cylindrical outlets to infinity. Kyushu J. Math. 53 (1999), 369–394.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Novotny. On steady transport equation. Advanced Topics in Theoretical Fluid Mechanics, Pitman Research Notes in Mathematics, J. Malek, J. Necas, M. Rokyta (Eds.), 392 (1998), 118–146.

    Google Scholar 

  13. A. Novotny. About steady transport equation II, Shauder estimates in domains with smooth boundaries. Portugaliae Mathematica, 54(3) (1997), 317–333.

    MathSciNet  MATH  Google Scholar 

  14. A. Novotny and M. Padula. Physically reasonable solutions to steady compressible Navier—Stokes equations in 3D-exterior domains I (vim = 0). J. Math. Kyoto Univ. 36(2) (1996), 389–423.

    MathSciNet  MATH  Google Scholar 

  15. A. Novotny and K. Pileckas. Steady compressible Navier—Stokes equations with large potential forces via a method of decomposition. Math. Meth. in Appl. Sci. 21 (1998), 665–684.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. V.A. Solonnikov. On the solvability of boundary and initial-boundary value problems for the Navier—Stokes system in domains with noncompact boundaries. Pacific J. Math. 93(2) (1981), 443–458.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius, Akademijos 4 2600, Lithuania

    T. Leonavičienė & K. Pileckas

Authors
  1. T. Leonavičienė
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  2. K. Pileckas
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Editor information

Editors and Affiliations

  1. School of Engineering Department of Mechanical Engineering, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    Giovanni P. Galdi

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Y4

    John G. Heywood

  3. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120, Heidelberg, Germany

    Rolf Rannacher

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Leonavičienė, T., Pileckas, K. (2004). Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow. In: Galdi, G.P., Heywood, J.G., Rannacher, R. (eds) Contributions to Current Challenges in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7877-7_5

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  • DOI: https://doi.org/10.1007/978-3-0348-7877-7_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9606-1

  • Online ISBN: 978-3-0348-7877-7

  • eBook Packages: Springer Book Archive

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