Klainerman, Sergiu; Majda, Andrew Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. (English) Zbl 0476.76068 Commun. Pure Appl. Math. 34, 481-524 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 443 Documents MSC: 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76W05 Magnetohydrodynamics and electrohydrodynamics 35L60 First-order nonlinear hyperbolic equations 35A10 Cauchy-Kovalevskaya theorems 35Q30 Navier-Stokes equations Keywords:limiting behavior; quasilinear hyperbolic systems; singular limits; constructive local existence theorems; time-singular limit equations; incompressible limits PDF BibTeX XML Cite \textit{S. Klainerman} and \textit{A. Majda}, Commun. Pure Appl. Math. 34, 481--524 (1981; Zbl 0476.76068) Full Text: DOI References: [1] Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974, p. 421. [2] Waves in Fluids, Cambridge University Press, Cambridge, 1978. · Zbl 0375.76001 [3] Kato, Arch. Rational Mech. Anal. 58 pp 181– (1975) [4] Kato, J. Funct. Anal. 9 pp 296– (1972) [5] Navier Stokes Equations, North Holland, Amsterdam, 1977. [6] Moser, Ann. Scuola Norm. Pisa 3 pp 265– (1966) [7] Klainerman, Comm. Pure Appl. Math. 33 pp 43– (1980) [8] Numerical solutions of hyperbolic systems with different time scales using asymptotic expansions, Applications to the M.H.D. Equations, Uppsala Report #74, May, 1978. [9] Problems with different time scales for ordinary differential equations, Uppsala Report #68, October 1977. [10] Kreiss, Comm. Pure Appl. Math. 33 pp 3– (1980) [11] Hoppensteadt, Comm. Pure Appl. Math. 26 pp 807– [12] Veiga, Rend. Sem. Mat. Univ. Padova 59 pp 115– (1978) [13] Chorin, J. Computational Phys. 2 pp 12– (1967) [14] Marsden, Comm. Partial Differential Equations 1 pp 215– (1976) [15] Ebin, Annals of Math. 150 pp 141– (1977) [16] Ebin, Ann. of Math. 92 pp 102– (1970) [17] Friedrichs, Comm. Pure Appl. Math. 7 pp 345– (1954) [18] Morawetz, Amer. Math. Monthly 85 pp 548– (1978) [19] Howe, J. Fluid Mech. 71 pp 626– (1975) [20] , and , (Eds.), Data Assimilation and Initialization in Dynamic Meterology, Springer-Verlag, in press. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.