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On Stability and Bifurcation in Parallel Flows of Compressible Navier-Stokes Equations

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Nonlinear Partial Differential Equations for Future Applications (PDEFA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 346))

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Abstract

The stability analysis of parallel flows of the compressible Navier-Stokes equations is overviewed. The asymptotic behaviour of solutions is firstly considered for small Reynolds and Mach numbers. An instability result of the plane Poiseuille flow is then given for a certain range of Reynolds and Mach numbers, together with a result of the bifurcation of wave trains from the plane Poiseuille flow.

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Acknowledgements

The author would like to thank Professor Shigeaki Koike, Professor Shigeru Sakaguchi, Professor Hideo Kozono and Professor Takayoshi Ogawa for their kindly inviting him to Thematic Programs “Nonlinear Partial Differential Equations for Future Applications”, Tohoku Forum for Creativity, July, 2017, Tohoku University. The author also would like to thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Yoshiyuki Kagei

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  1. Yoshiyuki Kagei
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Correspondence to Yoshiyuki Kagei .

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Editors and Affiliations

  1. Department of Applied Physics, Waseda University, Tokyo, Japan

    Shigeaki Koike

  2. Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono

  3. Mathematical Institute, Tohoku University, Sendai, Japan

    Takayoshi Ogawa

  4. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Shigeru Sakaguchi

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Kagei, Y. (2021). On Stability and Bifurcation in Parallel Flows of Compressible Navier-Stokes Equations. In: Koike, S., Kozono, H., Ogawa, T., Sakaguchi, S. (eds) Nonlinear Partial Differential Equations for Future Applications. PDEFA 2017. Springer Proceedings in Mathematics & Statistics, vol 346. Springer, Singapore. https://doi.org/10.1007/978-981-33-4822-6_2

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