References
- Gasser I, Markowich PA. Quantum hydrodynamics, Wigner transforms and the classical limit. Asymptot Anal. 1997;14:97–116.
- Dunn JE, Serrin J. On the thermomechanics of interstitial working. Arch Rational Mech Anal. 1985;88:95–133.
- Benzoni-Gavage S, Danchin R, Descombes S, et al. Structure of Korteweg models and stability of diffuse interfaces. Interface Free Boundaries. 2005;7:371–414.
- Benzoni-Gavage S. Propagating phase boundaries and capillary fluids. Lecture notes of CIRM summer school Mathematical Fluid Dynamics. Levico; 2010. p. 57.
- Benzoni-Gavage S, Danchin R, Descombes S. On the well-posedness for the Euler--Korteweg model in several space dimensions. Indiana Univ Math J. 2007;56:1499–1579.
- Giesselmann J, Lattanzio C, Tzavaras AE. Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics. Arch Rational Mech Anal. 2015. Forthcoming. Available from: http://arxiv.org/abs/1510.00801.
- Dafermos CM. The second law of thermodynamics and stability. Arch Rational Mech Anal. 1979;70:167–179.
- Dafermos CM. Stability of motions of thermoelastic fluids. J Therm Stresses. 1979;2:127–134.
- DiPerna RJ. Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ Math J. 1979;28:137–188.
- Donatelli D, Feireisl E, Marcati P. Well/ill posedness for the Euler--Korteweg--Poisson system and related problems. Commun Partial Differ Equ. 2015;40:1314–1335.
- Lattanzio C, Tzavaras AE. From gas dynamics with large friction to gradient flows describing diffusion theories. Comm Partial Diff Equations. 2015. Forthcoming. Available from: https://arxiv.org/abs/1601.05966.
- Charve F, Haspot B. Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system. SIAM J Math Anal. 2013;45(2):469–494.
- Germain P, LeFloch P. Finite energy method for compressible fluids: the Navier--Stokes--Korteweg model. Commun Pur Appl Math. 2016;69(1):3–61.
- Bedjaoui N, LeFloch PG. Diffusive-dispersive traveling waves and kinetic relations. IV. Compressible Euler equations. Chin Ann Math Ser B. 2003;24(1):17–34.
- Giesselmann J. A relative entropy approach to convergence of a low order approximation to a nonlinear elasticity model with viscosity and capillarity. SIAM J Math Anal. 2014;46:3518–3539.
- Lattanzio Corrado, Tzavaras Athanasios E. Relative entropy in diffusive relaxation. SIAM J Math Anal. 2013;45:1563–1584.