References
- Bouchut, F., Mangeney-Castelnau, A., Perthame, B., Vilotte, J.-P. (2003). A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows. C. R. Math. Acad. Sci. Paris 336:531–536.
- Bouchut, F., Westdickenberg, M. (2004). Gravity driven shallow water models for arbitrary topography. Commun. Math. Sci. 2:359–389.
- Chiodaroli, E. (2014). A counterexample to well-posedness of entropy solutions to the compressible Euler system. J. Hyperbolic Differ. Eqs. 11:493–519.
- Chiodaroli, E., Feireisl, E., Kreml, O. (2015). On the weak solutions to the equations of a compressible heat conducting gas. Ann. Inst. H. Poincaré Anal. Non Linéaire 32:225–243.
- Chiodaroli, E., Kreml, O. (2014). On the energy dissipation rate of solutions to the compressible isentropic Euler system. Arch. Rational Mech. Anal. 214:1019–1049.
- Dafermos, C. M. (1979). The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70:167–179.
- De Lellis, C., Székelyhidi, L., Jr. (2010). On admissibility criteria for weak solutions of the Euler equations. Arch. Rational Mech. Anal. 195:225–260.
- Desvillettes, L., Villani, C. (2005). On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation. Invent. Math. 159:245–316.
- DiPerna, R. J., Majda, A. J. (1987). Oscillations and concentrations in weak solutions of the incompressible fluid equations. Commun. Math. Phys. 108:667–689.
- Donatelli, D., Feireisl, E., Marcati, P. (2015). Well/ill posedness for the Euler-Korteweg-Poisson system and related problems. Commun. Partial Differ. Equations 40:1314–1335.
- Feireisl, E., Jin, B. J., Novotný, A. (2012). Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system. J. Math. Fluid Mech. 14:712–730.
- Feireisl, E. (2015). Weak solutions to problems involving inviscid fluids. IM Preprint No 2-2015.
- Fernández-Nieto, E. D., Bouchut, F., Bresch, D., Castro Daz, M. J., Mangeney, A. (2008). A new Savage–Hutter type model for submarine avalanches and generated tsunami. J. Comput. Phys. 227:7720–7754.
- Gray, J. M. N. T., Cui, X. (2007). Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows. J. Fluid Mech. 579:113–136.
- Gray, J. M. N. T., Tai, Y.-C., Noelle, S. (2003). Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491:161–181.
- Gwiazda, P. (2002). An existence result for a model of granular material with non-constant density. Asymptot. Anal. 30:43–60.
- Gwiazda, P. (2005). On measure-valued solutions to a two-dimensional gravity-driven avalanche flow model. Math. Methods Appl. Sci. 28:2201–2223.
- Hutter, K., Wang, Y., Pudasaini, S. P. (2005). The Savage–Hutter avalanche model: How far can it be pushed? Philos. Trans. R. Soc. London Ser. A Math. Phys. Eng. Sci. 363:1507–1528.
- Juez, C., Murillo, J., Garca-Navarro, P. (2013). 2D simulation of granular flow over irregular steep slopes using global and local coordinates. J. Comput. Phys. 255:166–204.
- Pelanti, M., Bouchut, F., Mangeney, A. (2008). A Roe-type scheme for two-phase shallow granular flows over variable topography. M2AN Math. Modell. Numer. Anal. 42:851–885.
- Scheffer, V. (1993). An inviscid flow with compact support in space-time. J. Geom. Anal. 3:343–401.
- Shnirelman, A. (1997). On the nonuniqueness of weak solution of the Euler equation. Commun. Pure Appl. Math. 50:1261–1286.
- Wiedemann, E. (2011). Existence of weak solutions for the incompressible Euler equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 28:727–730.
- Zahibo, N., Pelinovsky, E., Talipova, T., Nikolkin, I. (2010). Savage–Hutter model for avalanche dynamics in inclined channels: Analytical solutions. J. Geophys. Res. 115: B3402, 1–18.