EXISTENCE AND STABILITY OF NONMONOTONE HYDRAULIC SHOCKS FOR THE SAINT VENANT EQUATIONS OF INCLINED THIN-FILM FLOW - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

EXISTENCE AND STABILITY OF NONMONOTONE HYDRAULIC SHOCKS FOR THE SAINT VENANT EQUATIONS OF INCLINED THIN-FILM FLOW

Grégory Faye
Zhao Yang
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Kevin Zumbrun
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Résumé

Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number 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.
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Dates et versions

hal-04165596 , version 1 (19-07-2023)

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Grégory Faye, L. Miguel Rodrigues, Zhao Yang, Kevin Zumbrun. EXISTENCE AND STABILITY OF NONMONOTONE HYDRAULIC SHOCKS FOR THE SAINT VENANT EQUATIONS OF INCLINED THIN-FILM FLOW. 2023. ⟨hal-04165596⟩
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