期刊
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 368, 期 1916, 页码 1579-1593出版社
ROYAL SOC
DOI: 10.1098/rsta.2009.0283
关键词
Hamiltonian formulations; shock wave interactions and shock effects; control theory; convex sets and geometric inequalities; singularity theory
资金
- NSERC
- Russian Foundation for Basic Research [RFBR-CNRS-07-01-92217]
- French Agence Nationale de la Recherche [ANR-07-BLAN-0235 OTARIE]
- French Ministry for National Education
- Direct For Mathematical & Physical Scien
- Division Of Physics [923838] Funding Source: National Science Foundation
The characteristic curves of a Hamilton-Jacobi equation can be seen as action-minimizing trajectories of fluid particles. For non-smooth '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 non-smooth coalescing flow that extends particle trajectories and determines the dynamics inside shocks. We also provide a variational description of the corresponding effective velocity field inside shocks, and discuss the relation to the 'dissipative anomaly' in the limit of vanishing viscosity.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据