Particle dynamics inside shocks in Hamilton-Jacobi equations

Particle dynamics inside shocks in Hamilton-Jacobi equations

Characteristics of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. For nonsmooth "viscosity" solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and...

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Veröffentlicht in:arXiv.org 2010-01
Hauptverfasser: Khanin, Kostya, Sobolevski, Andrei
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Coalescing
Hamilton-Jacobi equation
Mathematics - Mathematical Physics
Particle trajectories
Physics - Mathematical Physics
Velocity distribution
Viscosity
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description Characteristics of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. For nonsmooth "viscosity" solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that for any convex Hamiltonian there exists a uniquely defined canonical global nonsmooth coalescing flow that extends particle trajectories and determines dynamics inside the shocks. We also provide a variational description of the corresponding effective velocity field inside shocks, and discuss relation to the "dissipative anomaly" in the limit of vanishing viscosity.
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subjects Coalescing
Hamilton-Jacobi equation
Mathematics - Mathematical Physics
Particle trajectories
Physics - Mathematical Physics
Velocity distribution
Viscosity
title Particle dynamics inside shocks in Hamilton-Jacobi equations
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