Commentary: Three decades after Cathleen Synge Morawetz’s paper “The mathematical approach to the sonic barrier”
HTML articles powered by AMS MathViewer
- by Irene M. Gamba PDF
- Bull. Amer. Math. Soc. 55 (2018), 347-350 Request permission
Abstract:
Immediately following the commentary below, this previously published article is reprinted in its entirety: Cathleen Synge Morawetz, “The mathematical approach to the sonic barrier”, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 127–145.References
- Gui-Qiang Chen and Mikhail Feldman, Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type, J. Amer. Math. Soc. 16 (2003), no. 3, 461–494. MR 1969202, DOI 10.1090/S0894-0347-03-00422-3
- Gui-Qiang Chen and Mikhail Feldman, Steady transonic shocks and free boundary problems for the Euler equations in infinite cylinders, Comm. Pure Appl. Math. 57 (2004), no. 3, 310–356. MR 2020107, DOI 10.1002/cpa.3042
- K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 333–418. MR 100718, DOI 10.1002/cpa.3160110306
- Irene M. Gamba, An existence and uniqueness result of a nonlinear two-dimensional elliptic boundary value problem, Comm. Pure Appl. Math. 48 (1995), no. 7, 669–689. MR 1342379, DOI 10.1002/cpa.3160480702
- Irene M. Gamba, Sharp uniform bounds for steady potential fluid-Poisson systems, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), no. 3, 479–516. MR 1453279, DOI 10.1017/S0308210500029887
- Irene M. Gamba and Cathleen S. Morawetz, A viscous approximation for a $2$-D steady semiconductor or transonic gas dynamic flow: existence theorem for potential flow, Comm. Pure Appl. Math. 49 (1996), no. 10, 999–1049. MR 1404324, DOI 10.1002/(SICI)1097-0312(199610)49:10<999::AID-CPA1>3.3.CO;2-W
- I. M. Gamba and C. S. Morawetz, Viscous approximation to transonic gas dynamics: flow past profiles and charged-particle systems, Modelling and computation for applications in mathematics, science, and engineering (Evanston, IL, 1996) Numer. Math. Sci. Comput., Oxford Univ. Press, New York, 1998, pp. 81–102. MR 1677377
- Cathleen S. Morawetz, On the non-existence of continuous transonic flows past profiles. I, Comm. Pure Appl. Math. 9 (1956), 45–68. MR 78130, DOI 10.1002/cpa.3160090104
- Cathleen S. Morawetz, A weak solution for a system of equations of elliptic-hyperbolic type, Comm. Pure Appl. Math. 11 (1958), 315–331. MR 96893, DOI 10.1002/cpa.3160110305
- Cathleen S. Morawetz, The Dirichlet problem for the Tricomi equation, Comm. Pure Appl. Math. 23 (1970), 587–601. MR 280062, DOI 10.1002/cpa.3160230404
- Cathleen Synge Morawetz, The mathematical approach to the sonic barrier, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 127–145. MR 640941, DOI 10.1090/S0273-0979-1982-14965-5
- Cathleen S. Morawetz, On a weak solution for a transonic flow problem, Comm. Pure Appl. Math. 38 (1985), no. 6, 797–817. MR 812348, DOI 10.1002/cpa.3160380610
- Cathleen S. Morawetz, Transonic flow and compensated compactness, Wave motion: theory, modelling, and computation (Berkeley, Calif., 1986) Math. Sci. Res. Inst. Publ., vol. 7, Springer, New York, 1987, pp. 248–258. MR 920838, DOI 10.1007/978-1-4613-9583-6_{9}
- Cathleen S. Morawetz, An alternative proof of DiPerna’s theorem, Comm. Pure Appl. Math. 44 (1991), no. 8-9, 1081–1090. MR 1127051, DOI 10.1002/cpa.3160440818
- Cathleen S. Morawetz, On steady transonic flow by compensated compactness, Methods Appl. Anal. 2 (1995), no. 3, 257–268. MR 1362016, DOI 10.4310/MAA.1995.v2.n3.a1
- Cathleen Synge Morawetz, Mixed equations and transonic flow, J. Hyperbolic Differ. Equ. 1 (2004), no. 1, 1–26. MR 2052469, DOI 10.1142/S0219891604000081
Additional Information
- Irene M. Gamba
- Affiliation: Department of Mathematics and The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas
- MR Author ID: 241132
- Email: gamba@math.utexas.edu
- Received by editor(s): April 9, 2018
- Published electronically: April 19, 2018
- Additional Notes: The author was supported by NSF grant no. DMS-1715515.
- © Copyright 2018 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 55 (2018), 347-350
- MSC (2010): Primary 35F20, 35F21, 35M10, 35Q30, 35Q35, 76H05
- DOI: https://doi.org/10.1090/bull/1620
- MathSciNet review: 3803158