Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow
Year: 2024
Type: article
Abstract: Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude number $$F<2$$ F < 2 , we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams, are all rigorously obtained by mathematical analysis and explicit calculation.
Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Institut National des Sciences Appliquées de Toulouse, Université de Toulouse, Institut de Mathématiques de Toulouse, Institut de recherche mathématique de Rennes, Université de Rennes, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Indiana University Bloomington, Indiana University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Awards: G2203179303, Frontiers in Modulation, Dynamics, and Pattern Formation for Hyperbolic, Kinetic, and Convection-Reaction-Diffusion Systems, New problems in continuum mechanics: asymptotic eigenvalue distributions, rigorous numerical stability analysis and weakly nonlinear asymptotics in periodic thin film flow, G325174859, Invasion dynamics and non-trivial asymptotics, G3341554066, G3691759950, G4414853111, Isaac Newton Institute for Mathematical Sciences, G7505370017, Centre International de Mathématiques et d'Informatique (de Toulouse), New Tools in the Study of Wave Propagation: Dynamical Systems for Kinetic Equations, Inviscid Limits for Modulated Periodic Waves, and Rigorous Numerical Stability Analysis
OpenAlex ID: W4384817462