Von Neumann’s comments about existence and uniqueness for the initial-boundary value problem in gas dynamics
HTML articles powered by AMS MathViewer
- by Denis Serre PDF
- Bull. Amer. Math. Soc. 47 (2010), 139-144 Request permission
References
- Alberto Bressan, Hyperbolic systems of conservation laws, Oxford Lecture Series in Mathematics and its Applications, vol. 20, Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. MR 1816648
- Gui-Qiang Chen and Mikhail Feldman, Potential theory for shock reflection by a large-angle wedge, Proc. Natl. Acad. Sci. USA 102 (2005), no. 43, 15368–15372. MR 2188921, DOI 10.1073/pnas.0505549102
- Ronald J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), no. 1, 1–30. MR 719807
- 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
- S. N. Kružkov, Generalized solutions of the Cauchy problem in the large for first order nonlinear equations, Dokl. Akad. Nauk. SSSR 187 (1969), 29–32 (Russian). MR 0249805
- P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI 10.1002/cpa.3160100406
- Jeffrey Rauch, BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one, Comm. Math. Phys. 106 (1986), no. 3, 481–484. MR 859822
Additional Information
- Denis Serre
- Affiliation: École Normale Supérieure de Lyon, D. S.: UMPA, CNRS UMR 5669. ENS de Lyon, 46 allée d’Italie. F-69364 Lyon, cedex 07, France
- MR Author ID: 158965
- Received by editor(s): September 8, 2009
- Published electronically: October 15, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 47 (2010), 139-144
- MSC (2010): Primary 01A60, 35L65, 35L67, 35Q35, 35Q85, 76N10, 76N15, 76P05, 85--03, 85A30
- DOI: https://doi.org/10.1090/S0273-0979-09-01286-5
- MathSciNet review: 2566448