참고문헌 (53)

1. L Ambrosio 2000 10.1093/oso/9780198502456.001.0001 Oxford mathematical monographs Functions of Bounded Variation and Free Discontinuity Problems Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford mathematical monographs. Oxford Press, Oxford (2000) 

   

2. Ann. Math. S Bianchini 166 223 2005 10.4007/annals.2005.161.223 Bianchini, S., Bressan, A.: Vanishing viscosity solutions to nolinear hyperbolic systems. Ann. Math. 166, 223-342 (2005) 

   

3. Commun. Math. Phys. D Bresch 238 211 2003 10.1007/s00220-003-0859-8 Bresch, D., Desjardins, B.: Existence of global weak solutions for 2d viscous shallow water equations and convergence to the quasi-geostrophic model. Commun. Math. Phys. 238, 211-223 (2003) 

   상세보기

4. J. Math. Pures Appl. D Bresch 86 9 362 2006 10.1016/j.matpur.2006.06.005 Bresch, D., Desjardins, B.: On the construction of approximate solutions for the 2d viscous shallow water model and for compressible navier-stokes models. J. Math. Pures Appl. 86(9), 362-368 (2006) 

   상세보기

5. Comm. Partial Differ. Equ. D Bresch 28 843 2003 10.1081/PDE-120020499 Bresch, D., Desjardins, B., Lin, C.K.: On some compressible fluid models: Korteweg, lubrication, and shallow water systems. Comm. Partial Differ. Equ. 28, 843-868 (2003) 

   상세보기

6. S Chapman 1970 The Mathematical Theory of Non-uniform Gases 3 Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases, 3rd edn. Cambridge University Press, London (1970) 

7. Commun. Math. Phys. G-Q Chen 228 2 201 2002 10.1007/s002200200615 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) 

   상세보기

8. Commun. Pure Appl. Math. G-Q Chen 63 11 1469 2010 10.1002/cpa.20332 Chen, G.-Q., Perepelitsa, M.: Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow. Commun. Pure Appl. Math. 63(11), 1469-1504 (2010) 

   상세보기

9. J. Hyperbolic Differ. Equ. E Chiodaroli 11 3 493 2014 10.1142/S0219891614500143 Chiodaroli, E.: A counterexample to well-posedness of entropy solutions to the compressible Euler system. J. Hyperbolic Differ. Equ. 11(3), 493-519 (2014) 

   상세보기

10. Commun. Pure Appl. Math. E Chiodaroli 68 7 1157 2015 10.1002/cpa.21537 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) 

    상세보기

11. Ann. Inst. H. Poincaré Anal. Non Linaire E Chiodaroli 32 1 225 2015 10.1016/j.anihpc.2013.11.005 Chiodaroli, E., Feireisl, E., Kreml, O.: On the weak solutions to the equations of a compressible heat conducting gas. Ann. Inst. H. Poincaré Anal. Non Linaire 32(1), 225-243 (2015) 

    상세보기

12. Arch. Ration. Mech. Anal. E Chiodaroli 214 3 1019 2014 10.1007/s00205-014-0771-8 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) 

    상세보기

13. Math. Mod. Meth. Appl. Sci. K Choi 30 387 2020 10.1142/S0218202520500104 Choi, K., Kang, M.-J., Kwon, Y.-S., Vasseur, A.: Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. Math. Mod. Meth. Appl. Sci. 30, 387-437 (2020) 

    상세보기

14. SIAM J. Math. Anal. K Choi 47 1405 2015 10.1137/140961523 Choi, K., Vasseur, A.: Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method. SIAM J. Math. Anal. 47, 1405-1418 (2015) 

    상세보기

15. Ann. Inst. H. Poincaré Anal. Non Linéaire P Constantin 37 145 2020 10.1016/j.anihpc.2019.04.001 Constantin, P., Drivas, T.D., Nguyen, H.Q., Pasqualotto, F.: Compressible fluids and active potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 37, 145-180 (2020) 

    상세보기

16. Arch. Rational Mech. Anal. CM Dafermos 70 2 167 1979 10.1007/BF00250353 Dafermos, C.M.: The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70(2), 167-179 (1979) 

    상세보기

17. Ann. Math. C De Lellis 170 3 1417 2009 10.4007/annals.2009.170.1417 De Lellis, C., Székelyhidi, L.: The Euler equations as a differential inclusion. Ann. Math. 170(3), 1417-1436 (2009) 

    상세보기

18. Arch. Ration. Mech. Anal. C De Lellis 195 1 225 2010 10.1007/s00205-008-0201-x De Lellis, C., Székelyhidi, L.: On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195(1), 225-260 (2010) 

    상세보기

19. Indiana Univ. Math. J. RJ DiPerna 28 1 137 1979 10.1512/iumj.1979.28.28011 DiPerna, R.J.: Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ. Math. J. 28(1), 137-188 (1979) 

    

20. Arch. Rational Mech. Anal. RJ DiPerna 82 1 27 1983 10.1007/BF00251724 DiPerna, R.J.: Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82(1), 27-70 (1983) 

    상세보기

21. Commun. Math. Phys. RJ DiPerna 91 1 1983 10.1007/BF01206047 DiPerna, R.J.: Convergence of the viscosity method for isentropic gas dynamics. Commun. Math. Phys. 91, 1-30 (1983) 

    상세보기

22. 10.1090/cbms/074 Evans, L.C.: Weak convergence methods for nonlinear partial differential equations,. CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC 74, (1990) 

    

23. Commun. Math. Sci. E Feireisl 14 6 1535 2016 10.4310/CMS.2016.v14.n6.a4 Feireisl, E.: Vanishing dissipation limit for the Navier-Stokes-Fourier system. Commun. Math. Sci. 14(6), 1535-1551 (2016) 

    상세보기

24. Discrete Contin. Dyn. Syst. Ser. B J-F Gerbeau 1 1 89 2018 Gerbeau, J.-F., Perthame, B.: Derivation of viscous saint-venant system for laminar shallow water; numerical validation. Discrete Contin. Dyn. Syst. Ser. B 1(1), 89-102 (2018) 

25. Arch. Rational Mech. Anal. J Goodman 121 235 1992 10.1007/BF00410614 Goodman, J., Xin, Z.: Viscous limits for piecewise smooth solutions to systems of conservation laws. Arch. Rational Mech. Anal. 121, 235-265 (1992) 

    상세보기

26. Haspot, B.: New formulation of the compressible navier-stokes equations and parabolicity of the density,. arXiv:1411.5501 

27. Hyperbolic Prob. Theory Numer. Appl. Methods Appl. Anal. B Haspot 20 2 141 2013 Haspot, B.: Porous media, fast diffusion equations and the existence of global weak solution for the quasi-solution of compressible Navier-Stokes equations. Hyperbolic Prob. Theory Numer. Appl. Methods Appl. Anal. 20(2), 141-164 (2013) 

28. Haspot, B.: Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D,. posted on arXiv, (2014) 

29. Commun. Math. Sci. B Haspot 15 3 587 2017 10.4310/CMS.2017.v15.n3.a1 Haspot, B.: Weak-strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension. Commun. Math. Sci. 15(3), 587-591 (2017) 

    상세보기

30. Indiana Univ. Math. J. D Hoff 38 861 1989 10.1512/iumj.1989.38.38041 Hoff, D., Liu, T.P.: The inviscid limit for the Navier-Stokes equations of compressible isentropic flow with shock data. Indiana Univ. Math. J. 38, 861-915 (1989) 

    

31. Kang, M.-J.: $$L^2$$-type contraction for shocks of scalar viscous conservation laws with strictly convex flux. J. Math. Pures Appl. (To appear) 

32. Kinet. Relat. Models M-J Kang 11 1 107 2018 10.3934/krm.2018006 Kang, M.-J.: Non-contraction of intermediate admissible discontinuities for 3-D planar isentropic magnetohydrodynamics. Kinet. Relat. Models 11(1), 107-118 (2018) 

    상세보기

33. Kang, M.-J., Vasseur, A.: Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system. J. Eur. Math. Soc. (JEMS), To appear. https://arxiv.org/pdf/1712.07348.pdf 

34. Arch. Ration. Mech. Anal. M-J Kang 222 1 343 2016 10.1007/s00205-016-1003-1 Kang, M.-J., Vasseur, A.: Criteria on contractions for entropic discontinuities of systems of conservation laws. Arch. Ration. Mech. Anal. 222(1), 343-391 (2016) 

    상세보기

35. Annales de l’Institut Henri Poincaré (C) : Analyse non linéaire M-J Kang 34 1 139 2017 10.1016/j.anihpc.2015.10.004 Kang, M.-J., Vasseur, A.: $$L^2$$-contraction for shock waves of scalar viscous conservation laws. Annales de l’Institut Henri Poincaré (C) : Analyse non linéaire 34(1), 139-156 (2017) 

    상세보기

36. J. Nonlinear Sci. M-J Kang 30 1703 2020 10.1007/s00332-020-09622-z Kang, M.-J., Vasseur, A.: Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities. J. Nonlinear Sci. 30, 1703-1721 (2020) 

    상세보기

37. J. Differ. Equ. M-J Kang 267 2737 2019 10.1016/j.jde.2019.03.030 Kang, M.-J., Vasseur, A., Wang, Y.: $$L^2$$-contraction for planar shock waves of multi-dimensional scalar viscous conservation laws. J. Differ. Equ. 267, 2737-2791 (2019) 

    상세보기

38. Arch. Ration. Mech. Anal. N Leger 199 3 761 2011 10.1007/s00205-010-0341-7 Leger, N.: $$L^2$$ stability estimates for shock solutions of scalar conservation laws using the relative entropy method. Arch. Ration. Mech. Anal. 199(3), 761-778 (2011) 

    상세보기

39. Arch. Ration. Mech. Anal. N Leger 201 1 271 2011 10.1007/s00205-011-0431-1 Leger, N., Vasseur, A.: Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-BV perturbations. Arch. Ration. Mech. Anal. 201(1), 271-302 (2011) 

    상세보기

40. Methods Appl. Anal. A Matsumura 17 279 2010 10.4310/MAA.2010.v17.n3.a3 Matsumura, A., Wang, Y.: Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity. Methods Appl. Anal. 17, 279-290 (2010) 

    

41. 10.1137/060658199 Mellet, A., Vasseur, A.: Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. SIAM J. Math. Anal. 39(4):1344-1365 (2007/2008) 

    상세보기

42. J. Éc. Polytech. Math. D Serre 1 1 2014 10.5802/jep.1 Serre, D., Vasseur, A.: $$L^2$$-type contraction for systems of conservation laws. J. Éc. Polytech. Math. 1, 1-28 (2014) 

    상세보기

43. Contemp. Math. AMS D Serre 658 237 2016 10.1090/conm/658/13123 Serre, D., Vasseur, A.: About the relative entropy method for hyperbolic systems of conservation laws. Contemp. Math. AMS 658, 237-248 (2016) 

    

44. Discrete Contin. Dyn. Syst. D Serre 36 8 4569 2016 10.3934/dcds.2016.36.4569 Serre, D., Vasseur, A.: The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete Contin. Dyn. Syst. 36(8), 4569-4577 (2016) 

    상세보기

45. 10.1016/0021-8928(84)90031-5 Shelukhin, V.V.: On the structure of generalized solutions of the one-dimensional equations of a polytropic viscous gas. J. Appl. Math. Mech., 48(1984), 665-672 

    상세보기

46. translated from Prikl. Mat. Mekh. 48(6), 912-920 (1984) 

47. Philos. Mag. GG Stokes 33 349 1848 Stokes, G.G.: On a difficulty in the theory of sound. Philos. Mag. 33, 349-356 (1848) 

48. Comm. Partial Differ. Equ. A Vasseur 24 11-12 1987 1999 10.1080/03605309908821491 Vasseur, A.: Time regularity for the system of isentropic gas dynamics with $$\gamma =3$$. Comm. Partial Differ. Equ. 24(11-12), 1987-1997 (1999) 

    상세보기

49. 10.1016/S1874-5717(08)00007-8 Vasseur, A.: Recent results on hydrodynamic limits. In: Handbook of differential equations: evolutionary equations. Vol. IV, Handbook Differential Equation, pp. 323-376. Elsevier/North-Holland, Amsterdam, (2008) 

    

50. 10.1090/conm/666/13296 Vasseur, A.: Relative entropy and contraction for extremal shocks of conservation laws up to a shift. In: Recent advances in partial differential equations and applications, volume 666 of Contemporary Mathematics, pages 385-404. American Mathematical Society, Providence, RI, (2016) 

    

51. SIAM J. Math. Anal. A Vasseur 47 6 4350 2015 10.1137/15M1023439 Vasseur, A., Wang, Y.: The inviscid limit to a contact discontinuity for the compressible navier-stokes-fourier system using the relative entropy method. SIAM J. Math. Anal. 47(6), 4350-4359 (2015) 

    상세보기

52. Commun. Math. Sci. A Vasseur 14 8 2215 2016 10.4310/CMS.2016.v14.n8.a5 Vasseur, A., Yao, L.: Nonlinear stability of viscous shock wave to one-dimensional compressible isentropic Navier-Stokes equations with density dependent viscous coefficient. Commun. Math. Sci. 14(8), 2215-2228 (2016) 

    상세보기

53. Arch. Rational Mech. Anal. SH Yu 146 275 1999 10.1007/s002050050143 Yu, S.H.: Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws. Arch. Rational Mech. Anal. 146, 275-370 (1999) 

    상세보기

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