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

Xiang Li (), Weiguo Zhang and Haipeng Jin
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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

Mathematics, 2023, vol. 11, issue 7, 1-11

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.

Keywords: nonlinear stability; monotone traveling wave; capillary term; non-convex pressure; weighted energy estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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