Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (4): 1041-1059.
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Received:
2021-08-12
Online:
2022-08-26
Published:
2022-08-08
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Boquan Fan. Desingularization of Karman Vortex Street[J].Acta mathematica scientia,Series A, 2022, 42(4): 1041-1059.
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1 |
Turkington B . On steady vortex flow in two dimensions I. Comm Partial Differential Equations, 1983, 8: 999- 1030
doi: 10.1080/03605308308820293 |
2 |
Turkington B . On steady vortex flow in two dimensions Ⅱ. Comm. Partial Differential Equations, 1983, 8: 1031- 1071
doi: 10.1080/03605308308820294 |
3 |
Turkington B . Corotating steady vortex flows with $N$-fold symmetry. Nonlinear Analysis, 1985, 9: 351- 369
doi: 10.1016/0362-546X(85)90059-8 |
4 |
Cao D , Peng S , Yan S . Planar vortex patch problem in incompressible steady flow. Adv Math, 2015, 270: 263- 301
doi: 10.1016/j.aim.2014.09.027 |
5 | Cao D , Wan J , Wang G . Nonlinear orbital stability for planar vortex patches. Proc Amer Math Soc, 2019, 147 (2): 775- 784 |
6 |
García C . Kármán vortex street in incompressible fluid models. Nonlinearity, 2020, 33 (4): 1625- 1676
doi: 10.1088/1361-6544/ab6309 |
7 |
Aref H . On the equilibrium and stability of a point vortices. J Fluid Mech, 1995, 290: 167- 181
doi: 10.1017/S002211209500245X |
8 | Lamb H . Hydrodynamics. Cambridge: Cambridge University Press, 1932 |
9 |
Pierrehumbert R T . A family of steady-translating vortex pairs with distributed vorticity. J Fluid Mech, 1980, 99: 129- 144
doi: 10.1017/S0022112080000559 |
10 | Lieb E H, Loss M. Analysis. Providence, RI: American Mathematical Society, 2001 |
11 |
Jimenez J . On the linear stability of the inviscid Kármán vortex street. J Fluid Mech, 1987, 178: 177- 194
doi: 10.1017/S0022112087001174 |
12 | Cao D, Lai S, Zhan W. Travelling vortex pairs for 2D incompressible Euler equations. To appear in Calc Var Partial Differential Equation |
13 | von Kármán T . Über den Mechanismus des Widerstands, den ein bewegter Korper in einer Flüssigkeit erfährt. Göttinger Nachr Math Phys Kl, 1911, 1: 509- 517 |
14 | von Kármán T . Über den Mechanismus des Widerstands, den ein bewegter Korper in einer Flüssigkeit erfährt. Göttinger Nachr Math Phys Kl, 1912, 2: 547- 556 |
15 |
Lin C C . On the motion of vortices in two dimension I. Existence of the Kirchhoff-Routh function. Proc Natl Acad Sci USA, 1941, 27: 570- 575
doi: 10.1073/pnas.27.12.570 |
16 | Strouhal V . Über eine besondere art der tonnerregung. Ann Phys Lpz, 1878, 5: 216- 251 |
17 |
Smets D , Van Schaftingen J . Desingularization of vortices for the Euler equation. Arch Rational Mech Anal, 2010, 198: 869- 925
doi: 10.1007/s00205-010-0293-y |
18 | Hmidi T , Mateu J . Existence of corotating and counter-rotating vortex pairs for active scalar equations. Comm Math Phys, 2017, 350: 699- 747 |
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