[1] T. Alazard, Incompressible limit of the nonisentropic Euler equations with the solid wall boundary conditions. Adv. Differential Equations, to appear. | Zbl | MR

[2] G. Alì, Low Mach number flows in time-dependent domains. SIAM J. Appl. Math. 63 (2003) 2020-2041. | Zbl

[3] K. Asano, On the incompressible limit of the compressible euler equation. Japan J. Appl. Math. 4 (1987) 455-488. | Zbl

[4] B.J. Bayly, C.D. Levermore and T. Passot, Density variations in weakly compressible flows. Phys. Fluids A 4 (1992) 945-954. | Zbl

[5] D. Bresch, B. Desjardins, E. Grenier and C.-K. Lin, Low Mach number limit of viscous polytropic flows: formal asymptotics in the periodic case. Stud. Appl. Math. 109 (2002) 125-149. | Zbl

[6] G. Browning and H.-O. Kreiss, Problems with different time scales for nonlinear partial differential equations. SIAM J. Appl. Math. 42 (1982) 704-718. | Zbl

[7] G. Browning, A. Kasahara and H.-O. Kreiss, Initialization of the primitive equations by the bounded derivative method. J. Atmospheric Sci. 37 (1980) 1424-1436.

[8] C. Cheverry, Justification de l'optique géométrique non linéaire pour un système de lois de conservation. Duke Math. J. 87 (1997) 213-263. | Zbl

[9] A. Chorin, A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2 (1967) 12-26. | Zbl

[10] R. Danchin, Zero Mach number limit for compressible flows with periodic boundary conditions. Amer. J. Math. 124 (2002) 1153-1219. | Zbl

[11] B. Desjardins and E. Grenier, Low Mach number limit of viscous compressible flows in the whole space. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999) 2271-2279. | Zbl

[12] B. Desjardins, E. Grenier, P.-L. Lions and N. Masmoudi, Incompressible limit for solutions of the isentropic navier-stokes equations with dirichlet boundary conditions. J. Math. Pures Appl. 78 (1999) 461-471. | Zbl

[13] A. Dutrifoy and T. Hmidi, The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data. C. R. Math. Acad. Sci. Paris 336 (2003) 471-474. | Zbl

[14] D. Ebin, The motion of slightly compressible fluids viewed as a motion with strong constraining force. Ann. Math. 105 (1977) 141-200. | Zbl

[15] D. Ebin, Motion of slightly compressible fluids in a bounded domain I. Comm. Pure Appl. Math. 35 (1982) 451-485. | Zbl

[16] I. Gallagher, Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation. J. Differential Equations 150 (1998) 363-384. | Zbl

[17] B. Gustafsson and H. Stoor, Navier-Stokes equations for almost incompressible flow. SIAM J. Numer. Anal. 28 (1991) 1523-1547. | Zbl

[18] T. Hagstrom and J. Lorenz, All-time existence of classical solutions for slightly compressible flows. SIAM J. Math. Anal. 29 (1998) 652-672. | Zbl

[19] T. Hagstrom and J. Lorenz, On the stability of approximate solutions of hyperbolic-parabolic systems and the all-time existence of smooth, slightly compressible flows. Indiana Univ. Math. J. 51 (2002) 1339-1387. | Zbl

[20] D. Hoff, The zero-Mach limit of compressible flows. Comm. Math. Phys. 192 (1998) 543-554. | Zbl

[21] T. Iguchi, The incompressible limit and the initial layer of the compressible Euler equation in $R_{+}^n$. Math. Methods Appl. Sci. 20 (1997) 945-958. | Zbl

[22] H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain. J. Reine Angew. Math. 381 (1987) 1-36. | Zbl

[23] H. Isozaki, Wave operators and the incompressible limit of the compressible Euler equation. Comm. Math. Phys. 110 (1987) 519-524. | Zbl

[24] H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain. II. Bodies in a uniform flow. Osaka J. Math. 26 (1989) 399-410. | Zbl

[25] J.-L. Joly, G. Métivier and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics. Ann. Sci. École Norm. Sup. (4) 28 (1995) 51-113. | Zbl | Numdam

[26] J.-L. Joly, G. Métivier and J. Rauch, Dense oscillations for the compressible 2-d Euler equations, in Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XIII (Paris, 1994/1996), Longman, Harlow. Pitman Res. Notes Math. Ser. 391 (1998) 134-166. | Zbl

[27] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58 (1975) 181-205. | Zbl

[28] S. Klainerman and A. Majda, Singular perturbations of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math. 34 (1981) 481-524. | Zbl

[29] S. Klainerman and A. Majda, Compressible and incompressible fluids. Comm. Pure Appl. Math. 35 (1982) 629-653. | Zbl

[30] R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I. One-dimensional flow. J. Comput. Phys. 121 (1995) 213-237. | Zbl

[31] R. Klein, N. Botta, T. Schneider, C.-D. Munz, S. Roller, A. Meister, L. Hoffmann and T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics. J. Engrg. Math. 39 (2001) 261-343. | Zbl

[32] H.-O. Kreiss, Problems with different time scales for partial differential equations. Comm. Pure Appl. Math. 33 (1980) 399-439. | Zbl

[33] C.K. Lin, On the incompressible limit of the compressible navier-stokes equations. Comm. Partial Differential Equations 20 (1995) 677-707. | Zbl

[34] P.-L. Lions, Mathematical topics in fluid mechanics, Vol. 1, Oxford Lecture Series in Mathematics and its Applications. The Clarendon Press Oxford University Press, New York 3 (1996). | Zbl | MR

[35] P.-L. Lions and N. Masmoudi, Incompressible limit for a viscous compressible fluid. J. Math. Pures Appl. 77 (1998) 585-627. | Zbl

[36] P.-L. Lions and N. Masmoudi, Une approche locale de la limite incompressible. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 387-392. | Zbl

[37] A. Meister, Asymptotic single and multiple scale expansions in the low Mach number limit. SIAM J. Appl. Math. 60 (2000) 256-271. | Zbl

[38] G. Métivier and S. Schochet, The incompressible limit of the non-isentropic euler equations. Arch. Rational Mech. Anal. 158 (2001) 61-90. | Zbl

[39] G. Métivier and S. Schochet, Averaging theorems for conservative systems and the weakly compressible Euler equations. J. Differential Equations 187 (2003) 106-183. | Zbl

[40] B. Müller, Low-Mach-number asymptotics of the Navier-Stokes equations. J. Engrg. Math. 34 (1998) 97-109. | Zbl

[41] M. Schiffer, Analytical theory of subsonic and supersonic flows, in Handbuch der Physik. Springer-Verlag, Berlin 9 (1960) 1-161.

[42] S. Schochet, The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit. Comm. Math. Phys. 104 (1986) 49-75. | Zbl

[43] S. Schochet, Asymptotics for symmetric hyperbolic systems with a large parameter. J. Differential Equations 75 (1988) 1-27. | Zbl

[44] S. Schochet, Fast singular limits of hyperbolic PDEs. J. Differential Equations 114 (1994) 476-512. | Zbl

[45] P. Secchi, On the singular incompressible limit of inviscid compressible fluids. J. Math. Fluid Mech. 2 (2000) 107-125. | Zbl

[46] T. Sideris, The lifespan of smooth solutions to the three-dimensional compressible Euler equations and the incompressible limit. Indiana Univ. Math J. 40 (1991) 535-550. | Zbl

[47] L. Sirovich, Initial and boundary value problems in dissipative gas dynamics. Phys. Fluids 10 (1967) 24-34. | Zbl

[48] R. Temam, Navier-Stokes equations. Theory and numerical analysis. North-Holland Publishing Co., Amsterdam (1977). | Zbl | MR

[49] S. Ukai, The incompressible limit and initial layer of the compressible Euler equation. J. Math. Kyoto U. 26 (1986) 323-331. | Zbl

[50] P.S. Van Der Gulik, The linear pressure dependence of the viscosity at high densities. Physica A 256 (1998) 39-56.

[51] M. Van Dyke, Perturbation methods in fluid mechanics. Appl. Math. Mech. 8. Academic Press, New York (1964). | Zbl | MR

[52] G.P. Zank and W.H. Matthaeus, The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves. Phys. Fluids A 3 (1991) 69-82. | Zbl