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Nonlinear Stability of the Monotone Traveling Wave for the Isothermal Fluid Equations with Viscous and Capillary Terms

Author

Listed:
  • Xiang Li

    (School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Weiguo Zhang

    (School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Haipeng Jin

    (State Grid Fuxin Electric Power Supply Company, Fuxin 123000, China)

Abstract

We prove the existence of the monotone traveling wave for the isothermal fluid equations with viscous and capillary terms by the planar dynamical system method. We obtain that the monotone traveling wave is asymptotically stable under the suitable perturbation. In the process of establishing the uniform a priori estimate, we dispose the capillary term reasonably according to the feature of the equations, and find the appropriate weighted function to overcome the difficulty caused by the non-convex pressure function.

Suggested Citation

  • Xiang Li & Weiguo Zhang & Haipeng Jin, 2023. "Nonlinear Stability of the Monotone Traveling Wave for the Isothermal Fluid Equations with Viscous and Capillary Terms," Mathematics, MDPI, vol. 11(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1734-:d:1116306
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    Cited by:

    1. Yuli D. Chashechkin & Artem A. Ochirov, 2023. "Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field," Mathematics, MDPI, vol. 11(21), pages 1-18, October.

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