Note on Lagrangian-Eulerian Methods for Uniqueness in Hydrodynamic Systems

2018/11/30 by Peter Constantin, Constantin, Peter, Joonhyun La +1
Mathematics · Engineering · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.1812.00039

Abstract

We discuss the Lagrangian-Eulerian framework for hydrodynamic models and provide a proof of Lipschitz dependence of solutions on initial data in path space. The paper presents a corrected version of the result in \citec1.

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• Existence and Uniqueness of Solutions to the Generalized Hydrodynamics Equation