References
- D. W. Ambrose, Well-posedness of vortex sheets with surface tension, SIAM J. Math. Anal. 35 (2003), no. 1, 211-244. https://doi.org/10.1137/S0036141002403869
- G. R. Baker and M. J. Shelley, On the connection between thin vortex layers and vortex sheets, J. Fluid Mech. 215 (1990), 161-194. https://doi.org/10.1017/S0022112090002609
- G. Birkhoff, Helmholtz and Taylor instability, Proceedings of Symposia in Applied Mathematics, Vol. XIII, 55-76, American Mathematical Society, Providence, 1962.
- W.-S. Dai and M. J. Shelley, A numerical study of the effect of surface tension and noise on an expanding Hele-Shaw bubble, Phys. Fluids A 5 (1993), 2131-2146. https://doi.org/10.1063/1.858553
- J.-M. Delort, Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc. 4 (1991), no. 3, 553-586. https://doi.org/10.1090/S0894-0347-1991-1102579-6
- M. R. Dhanak, Equation of motion of a diffusing vortex sheet, J. Fluid Mech. 269 (1994), 265-281. https://doi.org/10.1017/S0022112094001552
- M. A. Fontelos and F. de la Hoz, Singularities in water waves and the Rayleigh-Taylor problem, J. Fluid Mech. 651 (2010), 211-239. https://doi.org/10.1017/S0022112009992710
- T. Y. Hou, G. Hu, and P. Zhang, Singularity formation in three-dimensional vortex sheets, Phys. Fluids 15 (2003), no. 1, 147-172. https://doi.org/10.1063/1.1526100
- F. de la Hoz, M. A. Fontelos, and L. Vega, The effect of surface tension on the Moore singularity of vortex sheet dynamics, J. Nonlinear Sci. 18 (2008), no. 4, 463-484. https://doi.org/10.1007/s00332-008-9020-3
- S.-C. Kim, Evolution of a two-dimensional closed vortex sheet in a potential flow, J. Korean Phys. Soc. 46 (2005), 848-854.
- R. Krasny, A study of singularity formation in a vortex sheet by the point-vortex approximation, J. Fluid Mech. 167 (1986), 65-93. https://doi.org/10.1017/S0022112086002732
- R. Krasny, Desingularization of periodic vortex sheet roll-up, J. Comput. Phys. 65 (1986), 292-313. https://doi.org/10.1016/0021-9991(86)90210-X
- J.-G. Liu and Z. Xin, Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheet data, Comm. Pure Appl. Math. 48 (1995), no. 6, 611-628. https://doi.org/10.1002/cpa.3160480603
- A. J. Majda, Remarks on weak solutions for vortex sheets with a distinguished sign, Indiana Univ. Math. J. 42 (1993), no. 3, 921-939. https://doi.org/10.1512/iumj.1993.42.42043
- D. W. Moore, The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proc. Roy. Soc. London Ser. A 365 (1979), no. 1720, 105-119. https://doi.org/10.1098/rspa.1979.0009
- M. Nitsche, Singularity formation in a cylindrical and a spherical vortex sheet, J. Comput. Phys.173 (2001), 208-230. https://doi.org/10.1006/jcph.2001.6872
- T. Sakajo, Formation of curvature singularity along vortex line in an axisymmetric vortex sheet, Phys. Fluids 14 (2002), 2886-2897. https://doi.org/10.1063/1.1491255
- T. Sakajo and H. Okamoto, An application of Draghicescu's fast summation method to vortex sheet motion, J. Phys. Soc. Japan 67 (1998), 462-470. https://doi.org/10.1143/JPSJ.67.462
- M. J. Shelley, A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method, J. Fluid Mech. 244 (1992), 493-526. https://doi.org/10.1017/S0022112092003161
- S. Shin, S.-I. Sohn, and W. Hwang, Simple and efficient numerical methods for vortex sheet motion with surface tension, Internat. J. Numer. Methods Fluids 74 (2014), no. 6, 422-438. https://doi.org/10.1002/fld.3857
- S.-I. Sohn, Singularity formation and nonlinear evolution of a viscous vortex sheet model, Phys. Fluids 25 (2013), 014106. https://doi.org/10.1063/1.4789460
- S.-I. Sohn, Two vortex-blob regularization models for vortex sheet motion, Phys. Fluids 26 (2014), 044105. https://doi.org/10.1063/1.4872027
- G. Tryggvason, W. J. A. Dahm, and K. Sbeih, Fine structure of vortex sheet rollup by viscous and inviscid simulation, ASME J. Fluids Eng. 113 (1991), 31-36. https://doi.org/10.1115/1.2926492
- S. Wu, Mathematical analysis of vortex sheets, Comm. Pure Appl. Math. 59 (2006), no. 8, 1065-1206. https://doi.org/10.1002/cpa.20110