On convergence of approximate solutions to the compressible Euler system

Alibert, J.J., Bouchitté, G.: Non-uniform integrability and generalized Young measures. J. Convex Anal. 4(1), 129–147 (1997)

Ball, J.M., Murat, F.: Remarks on Chacons biting lemma. Proc. Am. Math. Soc. 107, 655–663 (1989)

Basarić, D.: Vanishing viscosity limit for the compressible Navier-Stokes system via measure-valued solutions. Arxive Preprint Series, ArXiv:1903.05886, 2019 (1903)

Bechtel, S.E., Rooney, F.J., Forest, M.G.: Connection between stability, convexity of internal energy, and the second law for compressible Newtonian fuids. J. Appl. Mech. 72, 299–300 (2005)

Breit, D., Feireisl, E., Hofmanová, M.: Dissipative solutions and semiflow selection for the complete Euler system. Arxive Preprint Series, ArXiv:1904.00622: To appear in Commun. Math. Phys. (2019)

Buckmaster, T., Vicol, V.: Convex integration and phenomenologies in turbulence. Arxiv Preprint Series, 2019. ArXiv:1901.09023v2

Březina, J., Feireisl, E.: Measure-valued solutions to the complete Euler system. J. Math. Soc. Jpn. 70(4), 1227–1245 (2018)

Chen, G.-Q., Frid, H., Li, Y.: Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics. Commun. Math. Phys. 228(2), 201–217 (2002)

Chen, G.Q., Glimm, J.: Kolmogorov-type theory of compressible turbulence and inviscid limit of the Navier-Stokes equations in $${R}^3$$. Arxive Preprint Series, ArXiv:1809.09490, 2018 (1809)

Chiodaroli, E.: A counterexample to well-posedness of entropy solutions to the compressible Euler system. J. Hyperbolic Differ. Equ. 11(3), 493–519 (2014)

Chiodaroli, E., De Lellis, C., Kreml, O.: Global ill-posedness of the isentropic system of gas dynamics. Commun. Pure Appl. Math. 68(7), 1157–1190 (2015)

Chiodaroli, E., Kreml, O.: On the energy dissipation rate of solutions to the compressible isentropic Euler system. Arch. Ration. Mech. Anal. 214(3), 1019–1049 (2014)

Chiodaroli, E., Kreml, O., Mácha, V., Schwarzacher, S.: Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data. Arxiv Preprint Series, ArXiv:1812.09917v1, 2019

Constantin, P., Vicol, V.: Remarks on high Reynolds numbers hydrodynamics and the inviscid limit. J. Nonlinear Sci. 28(2), 711–724 (2018)

Dafermos, C.M.: The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70, 167–179 (1979)

De Lellis, C., Székelyhidi Jr., L.: On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195(1), 225–260 (2010)

DiPerna, R.J., Majda, A.: Reduced hausdorff dimension and concentration-cancellation for two dimensional incompressible flow. J. Am. Math. Soc. 1(1), 59–95 (1988)

DiPerna, R.J., Majda, A.J.: Concentrations in regularizations for 2-d incompressible flow. Commun. Pure Appl Math 40(3), 301–345 (1987)

DiPerna, R.J., Majda, A.: Reduced Hausdorff dimension and concentration cancellation for two-dimensional incompressible flow. J. Am. Math. Soc. 1, 59–95 (1988)

Feireisl, E.: Vanishing dissipation limit for the Navier-Stokes-Fourier system. Commun. Math. Sci. 14(6), 1535–1551 (2016)

Feireisl, E., Lukáčová-Medvidová, M.: Convergence of a mixed finite element finite volume scheme for the isentropic Navier–Stokes system via dissipative measure–valued solutions. 2017. arxiv preprint ArXiv:1608.06149

Feireisl, E., Lukáčová-Medvidová, M., Mizerová, H.: $${\cal{K}}-$$convergence as a new tool in numerical analysis. 2019. arxiv preprint ArXiv:1904.00297

Feireisl, E., Lukáčová-Medvidová, M., Mizerová, H., She, B., Wang, Y.: Computing oscillatory solutions to the Euler system via $${\cal{K}}$$-convergence. 2019. arxiv preprint ArXiv:1910.03161

Fjordholm, U.K., Käppeli, R., Mishra, S., Tadmor, E.: Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws. Found. Comp. Math. 17(3), 1–65 (2015)

Fjordholm, U.S., Lye, K., Mishra, S., Weber, F.: Statistical solutions of hyperbolic systems of conservation laws: numerical approximation. Arxive Preprint Series, ArXiv:1906.02536, 2019 (1906)

Fjordholm, U.S., Mishra, S., Tadmor, E.: On the computation of measure-valued solutions. Acta Numer. 25, 567–679 (2016)

Galdi, G.P.: An introduction to the mathematical theory of the Navier–Stokes equations. I. Springer, New York (1994)

Greengard, C., Thomann, E.: On DiPerna-Majda concentration sets for two-dimensional incompressible flow. Commun. Pure Appl. Math. 41(3), 295–303 (1988)

Gwiazda, P., Świerczewska-Gwiazda, A., Wiedemann, E.: Weak-strong uniqueness for measure-valued solutions of some compressible fluid models. Nonlinearity 28(11), 3873–3890 (2015)

Sprung, B.: Upper and lower bounds for the Bregman divergence. J. Inequal. Appl. 12, 4 (2019)

Sueur, F.: On the inviscid limit for the compressible Navier–Stokes system in an impermeable bounded domain. J. Math. Fluid Mech. 16(1), 163–178 (2014)

Wienan, E.: Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation. Acta Math. Sin. 16(2), 207–218 (2000)