Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The Euler Equations of Compressible Fluid Flow
HTML articles powered by AMS MathViewer

by Demetrios Christodoulou PDF
Bull. Amer. Math. Soc. 44 (2007), 581-602 Request permission
References
    [Be]Be Bernoulli, D. Hydrodynamica, Argentorati (1738). [Bo]Bo Boltzmann, L. “Über die Bezeihung zwischen dem zweiten Hauptsatzes der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respective den Sätzen über das Wärmegleichgewicht”, Wien Ber. 76, 73 (1877).
  • Demetrios Christodoulou, The formation of shocks in 3-dimensional fluids, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2007. MR 2284927, DOI 10.4171/031
  • Demetrios Christodoulou, The action principle and partial differential equations, Annals of Mathematics Studies, vol. 146, Princeton University Press, Princeton, NJ, 2000. MR 1739321, DOI 10.1515/9781400882687
  • Demetrios Christodoulou and Sergiu Klainerman, The global nonlinear stability of the Minkowski space, Princeton Mathematical Series, vol. 41, Princeton University Press, Princeton, NJ, 1993. MR 1316662
    • [Cl1]Cl1 Clausius, R. “Über die bewegende Kraft der Wärme”, Annalen der Physik und Chemie 79, 368-397, 500-524 (1850). [Cl2]Cl2 Clausius, R. “Über verschiedene fü die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie”, Annalen der Physik und Chemie 125, 353-400 (1865). [DA]DA D’Alembert, J.-B. le R. “Recherches sur la courbe que forme une corde tenduë mise en vibration”, Mém. Acad. Sci. Berlin 2, 214-219 (1849). [Ei]Ei Einstein, A. “Zur Electrodynamic bewegter Körper”, Annalem der Physik 17, 891-921 (1905). [Eu1]Eu1 Euler, L. “Principes generaux de l’etat d’equilibre des fluides”, Mémoires de l’Academie des Sciences de Berlin 11, 217-273 (1757). [Eu2]Eu2 Euler, L. “Principes generaux du mouvement des fluides”, Mémoires de l’Academie des Sciences de Berlin 11, 274-315 (1757). [Eu3]Eu3 Euler, L. “Continuation des recherrches sur la theorie du mouvement des fluides”, Mémoires de l’Academie des Sciences de Berlin 11, 316-361 (1757). [Eu4]Eu4 Euler, L. “Principia motus fluidorum”, Novi Commentarii Academiae Scientiarum Petropolitanae 6, 271-311 (1761). [Eu5]Eu5 Euler, L. “De motu fluidorum a diverso caloris gradu oriundo”, Novi Commentarii Academiae Scientiarum Petropolitanae 11, 232-267 (1767). [Eu6]Eu6 Euler, L. “Sectio secunda de principiis motus fluidorum”, Novi Commentarii Academiae Scientiarum Petropolitanae 14, 270-386 (1770). [Eu7]Eu7 Euler, L. “Sectio tertia de motu fluidorum lineari potissimum aquae”, Novi Commentarii Academiae Scientiarum Petropolitanae 15, 219-360 (1771). [Eu8]Eu8 Euler, L. “Sectio quarta de motu aeris in tubis”, Novi Commentarii Academiae Scientiarum Petropolitanae 16, 281-425 (1772).
  • K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345–392. MR 62932, DOI 10.1002/cpa.3160070206
  • K. O. Friedrichs and P. D. Lax, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 1686–1688. MR 285799, DOI 10.1073/pnas.68.8.1686
  • James Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697–715. MR 194770, DOI 10.1002/cpa.3160180408
    • [He]He Helmholtz, H. v. Über die Erhaltung der Kraft, G. Reimer, Berlin, 1847. [Hu]Hu Hugoniot, H. “Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits”, Journal de l’école polytechnique 58, 1-125 (1889).
  • Fritz John, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math. 27 (1974), 377–405. MR 369934, DOI 10.1002/cpa.3160270307
    • [Kr]Kr Kružhkov, S. N. “First order quasilinear equations in several independent variables”, Math. USSR Sbornik 10, No. 2 (1970).
  • Joseph B. Keller and Lu Ting, Periodic vibrations of systems governed by nonlinear partial differential equations, Comm. Pure Appl. Math. 19 (1966), 371–420. MR 205520, DOI 10.1002/cpa.3160190404
    • [La]La Laplace, P. S. “Sur la vitesse du son dans l’air et dans l’eau”, Ann. de Chim. et de Phys. iii, 238 (1816).
  • L. D. Landau and E. M. Lifshitz, Course of theoretical physics. Vol. 6, 2nd ed., Pergamon Press, Oxford, 1987. Fluid mechanics; Translated from the third Russian edition by J. B. Sykes and W. H. Reid. MR 961259
  • Peter Lax, Shock waves and entropy, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 603–634. MR 0393870
  • Peter D. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Mathematical Phys. 5 (1964), 611–613. MR 165243, DOI 10.1063/1.1704154
  • Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0350216
  • A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984. MR 748308, DOI 10.1007/978-1-4612-1116-7
    • [Ma2]Ma2 Majda, A. The Stability of Multi-Dimensional Shock Fronts - A New Problem for Linear Hyperbolic Equations, Mem. Amer. Math. Society 275, 1983.
  • Andrew Majda, The existence of multidimensional shock fronts, Mem. Amer. Math. Soc. 43 (1983), no. 281, v+93. MR 699241, DOI 10.1090/memo/0281
  • Andrew J. Majda and Andrea L. Bertozzi, Vorticity and incompressible flow, Cambridge Texts in Applied Mathematics, vol. 27, Cambridge University Press, Cambridge, 2002. MR 1867882
    • [Mi]Mi Minkowski, H. “Raum und Zeit”, Address at the 80th Assembly of German Natural Scientists and Physicians, Cologne (1908).
  • Cathleen S. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961), 561–568. MR 132908, DOI 10.1002/cpa.3160140327
    • [N]N Noether, E. “Invariante Variationsprobleme”, Nach. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1918, 235-257 (1918). [Ra]Ra Rankine, W.J.M. “On the thermodynamic theory of waves of finite longitudinal disturbance”, Philosophical Transactions of the Royal Society of London 160, 277-288 (1870). [Ri]Ri Riemann, B. “Über die Fortpfanzung ebener Luftwellen von endlicher Schwingungswete”, Abhandlungen der Gesellshaft der Wissenshaften zu Göttingen, Mathematisch-physikalishe Klasse 8, 43 (1858-59).
  • Thomas C. Sideris, Formation of singularities in three-dimensional compressible fluids, Comm. Math. Phys. 101 (1985), no. 4, 475–485. MR 815196, DOI 10.1007/BF01210741
    • [Z-R]Z-R Zel’dovich, Y.B., and Raizer, Y.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phaenomena, New York, 1966, 1967, Chapter I, Section 19, and Chapter XI, Section 20.
Similar Articles
Additional Information
  • Demetrios Christodoulou
  • Affiliation: Departments of Mathematics and Physics, ETH-Zürich, ETH-Zentrum, 8092 Zürich, Switzerland
  • Email: demetri@math.ethz.ch
  • Received by editor(s): May 15, 2007
  • Published electronically: June 18, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 44 (2007), 581-602
  • MSC (2000): Primary 76L05, 76-03; Secondary 01A50, 01A55, 01A60, 35L65, 35L67, 76N15
  • DOI: https://doi.org/10.1090/S0273-0979-07-01181-0
  • MathSciNet review: 2338367