Finite Energy Method for Compressible Fluids: The Navier‐Stokes‐Korteweg Model

2015/10/17 by Pierre Germain, Philippe LeFloch, Philippe G. LeFloch · 2 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · doi:10.1002/cpa.21622

Abstract

Abstract This is the first of a series of papers devoted to the initial value problem for the one‐dimensional Euler system of compressible fluids and augmented versions containing higher‐order terms. In the present paper, we are interested in dispersive shock waves and analyze the zero viscosity‐capillarity limit associated with the Navier‐Stokes‐Korteweg system. Specifically, we establish the existence of finite energy solutions as well as their convergence toward entropy solutions to the Euler system. Our method of proof combines energy and effective energy estimates, a nonlinear Sobolev inequality, high‐integrability properties for the mass density and for the velocity, and compactness properties based on entropies.© 2015 Wiley Periodicals, Inc.

Citations

• On the thermomechanics of interstitial working

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