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Compressible vortex sheets separating from solid boundaries
1. | Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, United States |
References:
[1] |
H. Alt, L. Caffarelli and A. Friedman, Compressible flow of jets and cavities, J. Diff. Eqs., 56 (1985), 82-141.
doi: 10.1016/0022-0396(85)90101-9. |
[2] |
G. Batchelor, An Introduction to Fluid Dynamics, Second paperback edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1999. |
[3] |
P. Berg, The existence of subsonic helmholtz flows of a compressible fluid, Comm. Pure Appl. Math., 15 (1962), 289-347.
doi: 10.1002/cpa.3160150302. |
[4] |
L. Bers, Existence and uniqueness of a subsonic flow past a given profile, Comm. Pure. Appl. Math., 7 (1954), 441-504.
doi: 10.1002/cpa.3160070303. |
[5] |
G.-Q. Chen, V. Kukreja and H. Yuan, Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible euler flows, Zeitschrift für angewandte Mathematik und Physik, 64 (2013), 1711-1727.
doi: 10.1007/s00033-013-0312-6. |
[6] |
A. Chorin and J. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer, 1992. |
[7] |
J. d'Alembert, Essai d'une nouvelle théorie de la résistance des fluides, 1752. |
[8] |
V. Elling, A possible counterexample to well-posedness of entropy solutions and to {Godunov} scheme convergence, Math. Comp., 75 (2006), 1721-1733.
doi: 10.1090/S0025-5718-06-01863-1. |
[9] |
V. Elling, Existence of algebraic vortex spirals, in Hyperbolic problems. Theory, Numerics and Applications., vol. 1 of Ser. Contemp. Appl. Math. CAM, 17, World Sci. Publishing, Singapore, 2012, 203-214. |
[10] |
R. Finn and D. Gilbarg, Asymptotic behaviour and uniqueness of plane subsonic flows, Comm. Pure Appl. Math., 10 (1957), 23-63.
doi: 10.1002/cpa.3160100102. |
[11] |
L. Föppl, Wirbelbewegung hinter einem Kreiszylinder, Sitz. K. Bayr. Akad. Wiss., 7-18. |
[12] |
H. Helmholtz, Über discontinuirliche Flüssigkeits-Bewegungen, Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 215-228. |
[13] |
G. Kirchhoff, Zur Theorie freier Flüssigkeitsstrahlen, J. Reine Angew. Math., 70 (1869), 289-298.
doi: 10.1515/crll.1869.70.289. |
[14] |
C. D. Lellis and L. S. Jr., On admissibility criteria for weak solutions of the Euler equations, Arch. Rat. Mech. Anal., 195 (2010), 225-260.
doi: 10.1007/s00205-008-0201-x. |
[15] |
T. Levi-Civita, Scie e leggi di resistenzia, Rend. Circ. Mat. Palermo, 23 (1907), 1-37. |
[16] |
M. Lopes-Filho, J. Lowengrub, H. N. Lopes and Y. Zheng, Numerical evidence of nonuniqueness in the evolution of vortex sheets, ESAIM:M2AN, 40 (2006), 225-237.
doi: 10.1051/m2an:2006012. |
[17] |
V. Maz'ya and B. Plamenevskii, Estimates in $L_p$ and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points, Amer. Math. Soc. Transl. (2), 123 (1984), 1-88. |
[18] |
D. Moore, The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 365 (1979), 105-119.
doi: 10.1098/rspa.1979.0009. |
[19] |
L. Prandtl, Über Flüssigkeitsbewegung bei sehr kleiner Reibung, in Verhandlungen des III. Internationalen Mathematiker-Kongresses, Heidelberg}, 1904. |
[20] |
D. Pullin, On similarity flows containing two-branched vortex sheets, in Mathematical aspect of vortex dynamics (ed. R. Caflisch), SIAM, 1989, 97-106. |
[21] |
L. Rayleigh, On the resistance of fluids, Phil. Mag., 11 (1876), 430-441. |
[22] |
A. Roshko, Perspectives on bluff body aerodynamics, Journal of Wind Engineering and Industrial Aerodynamics, 49 (1993), 79-100.
doi: 10.1016/0167-6105(93)90007-B. |
[23] |
P. Saffman, Vortex Dynamics, Cambridge University Press, 1992. |
[24] |
V. Scheffer, An inviscid flow with compact support in space-time, J. Geom. Anal., 3 (1993), 343-401.
doi: 10.1007/BF02921318. |
[25] |
M. Shiffman, On the existence of subsonic flows of a compressible fluid, J. Rat. Mech. Anal., 1 (1952), 605-652. |
[26] |
A. Shnirelman, On the nonuniqueness of weak solutions of the Euler equation, Comm. Pure Appl. Math., 50 (1997), 1261-1286.
doi: 10.1002/(SICI)1097-0312(199712)50:12<1261::AID-CPA3>3.0.CO;2-6. |
[27] |
J. Smith, Behaviour of a Vortex Sheet Separating from a Smooth Surface, Technical Report 77058, Royal Aircraft Establishment, 1977. |
[28] |
V. Sychev, Asymptotic theory of separation flows, Fluid Dynamics, 17 (1982), 20-30. |
[29] |
M. van Dyke, An Album of Fluid Motion, The Parabolic Press, Stanford, California, 1982. |
show all references
References:
[1] |
H. Alt, L. Caffarelli and A. Friedman, Compressible flow of jets and cavities, J. Diff. Eqs., 56 (1985), 82-141.
doi: 10.1016/0022-0396(85)90101-9. |
[2] |
G. Batchelor, An Introduction to Fluid Dynamics, Second paperback edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1999. |
[3] |
P. Berg, The existence of subsonic helmholtz flows of a compressible fluid, Comm. Pure Appl. Math., 15 (1962), 289-347.
doi: 10.1002/cpa.3160150302. |
[4] |
L. Bers, Existence and uniqueness of a subsonic flow past a given profile, Comm. Pure. Appl. Math., 7 (1954), 441-504.
doi: 10.1002/cpa.3160070303. |
[5] |
G.-Q. Chen, V. Kukreja and H. Yuan, Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible euler flows, Zeitschrift für angewandte Mathematik und Physik, 64 (2013), 1711-1727.
doi: 10.1007/s00033-013-0312-6. |
[6] |
A. Chorin and J. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer, 1992. |
[7] |
J. d'Alembert, Essai d'une nouvelle théorie de la résistance des fluides, 1752. |
[8] |
V. Elling, A possible counterexample to well-posedness of entropy solutions and to {Godunov} scheme convergence, Math. Comp., 75 (2006), 1721-1733.
doi: 10.1090/S0025-5718-06-01863-1. |
[9] |
V. Elling, Existence of algebraic vortex spirals, in Hyperbolic problems. Theory, Numerics and Applications., vol. 1 of Ser. Contemp. Appl. Math. CAM, 17, World Sci. Publishing, Singapore, 2012, 203-214. |
[10] |
R. Finn and D. Gilbarg, Asymptotic behaviour and uniqueness of plane subsonic flows, Comm. Pure Appl. Math., 10 (1957), 23-63.
doi: 10.1002/cpa.3160100102. |
[11] |
L. Föppl, Wirbelbewegung hinter einem Kreiszylinder, Sitz. K. Bayr. Akad. Wiss., 7-18. |
[12] |
H. Helmholtz, Über discontinuirliche Flüssigkeits-Bewegungen, Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 215-228. |
[13] |
G. Kirchhoff, Zur Theorie freier Flüssigkeitsstrahlen, J. Reine Angew. Math., 70 (1869), 289-298.
doi: 10.1515/crll.1869.70.289. |
[14] |
C. D. Lellis and L. S. Jr., On admissibility criteria for weak solutions of the Euler equations, Arch. Rat. Mech. Anal., 195 (2010), 225-260.
doi: 10.1007/s00205-008-0201-x. |
[15] |
T. Levi-Civita, Scie e leggi di resistenzia, Rend. Circ. Mat. Palermo, 23 (1907), 1-37. |
[16] |
M. Lopes-Filho, J. Lowengrub, H. N. Lopes and Y. Zheng, Numerical evidence of nonuniqueness in the evolution of vortex sheets, ESAIM:M2AN, 40 (2006), 225-237.
doi: 10.1051/m2an:2006012. |
[17] |
V. Maz'ya and B. Plamenevskii, Estimates in $L_p$ and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points, Amer. Math. Soc. Transl. (2), 123 (1984), 1-88. |
[18] |
D. Moore, The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 365 (1979), 105-119.
doi: 10.1098/rspa.1979.0009. |
[19] |
L. Prandtl, Über Flüssigkeitsbewegung bei sehr kleiner Reibung, in Verhandlungen des III. Internationalen Mathematiker-Kongresses, Heidelberg}, 1904. |
[20] |
D. Pullin, On similarity flows containing two-branched vortex sheets, in Mathematical aspect of vortex dynamics (ed. R. Caflisch), SIAM, 1989, 97-106. |
[21] |
L. Rayleigh, On the resistance of fluids, Phil. Mag., 11 (1876), 430-441. |
[22] |
A. Roshko, Perspectives on bluff body aerodynamics, Journal of Wind Engineering and Industrial Aerodynamics, 49 (1993), 79-100.
doi: 10.1016/0167-6105(93)90007-B. |
[23] |
P. Saffman, Vortex Dynamics, Cambridge University Press, 1992. |
[24] |
V. Scheffer, An inviscid flow with compact support in space-time, J. Geom. Anal., 3 (1993), 343-401.
doi: 10.1007/BF02921318. |
[25] |
M. Shiffman, On the existence of subsonic flows of a compressible fluid, J. Rat. Mech. Anal., 1 (1952), 605-652. |
[26] |
A. Shnirelman, On the nonuniqueness of weak solutions of the Euler equation, Comm. Pure Appl. Math., 50 (1997), 1261-1286.
doi: 10.1002/(SICI)1097-0312(199712)50:12<1261::AID-CPA3>3.0.CO;2-6. |
[27] |
J. Smith, Behaviour of a Vortex Sheet Separating from a Smooth Surface, Technical Report 77058, Royal Aircraft Establishment, 1977. |
[28] |
V. Sychev, Asymptotic theory of separation flows, Fluid Dynamics, 17 (1982), 20-30. |
[29] |
M. van Dyke, An Album of Fluid Motion, The Parabolic Press, Stanford, California, 1982. |
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