Lushnikov, Pavel M. Exactly integrable dynamics of interface between ideal fluid and light viscous fluid. (English) Zbl 1209.37103 Phys. Lett., A 329, No. 1-2, 49-54 (2004). Summary: It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between normal velocity and pressure at interface. Surface elevation and velocity potential of ideal fluid are determined from two complex Burgers equations corresponding to analytical continuation of velocity potential at the interface into upper and lower complex half planes, respectively. The interface loses its smoothness if complex singularities (poles) reach the interface. Cited in 5 Documents MSC: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology 76D07 Stokes and related (Oseen, etc.) flows 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:interface dynamics; integrable equation; Stokes flow; potential flow; complex Burgers equation PDFBibTeX XMLCite \textit{P. M. Lushnikov}, Phys. Lett., A 329, No. 1--2, 49--54 (2004; Zbl 1209.37103) Full Text: DOI arXiv References: [1] Howison, S. D.; Richardson, S., Eur. J. Appl. Math., 36, 441 (1995) [2] Kuznetsov, E. A.; Spector, M. D.; Zakharov, V. E., Phys. Rev. E, 49, 1283 (1994) [3] Dyachenko, A. I.; Zakharov, V. E.; Kuznetsov, E. A., Plasma Phys. Rep., 22, 829 (1996) [4] Kuznetsov, E. A.; Spector, M. D.; Zakharov, V. E., Phys. Lett. A, 182, 387 (1993) [5] Richardson, S., J. Fluid Mech., 56, 609 (1972) · Zbl 0256.76024 [6] Fokas, A. S.; Tanveer, S., Math. Proc. Cambridge Philos. Soc., 124, 169 (1998) [7] Mineev-Weinstein, M.; Wiegmann, P. B.; Zabrodin, A., Phys. Rev. Lett., 84, 5106 (2000) [8] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics (1989), Pergamon: Pergamon New York · Zbl 0146.22405 [9] Zakharov, V. E., J. Appl. Mech. Tech. Phys., 2, 190 (1968) [10] Cole, J. D., Quart. Appl. Math., 9, 225 (1951) [11] Ablowitz, M. J.; Fokas, A. S.; Kruskal, M. D., Phys. Lett. A, 120, 215 (1987) [12] Senouf, D., SIAM J. Math. Anal., 28, 1490 (1997) [13] Calogero, F., Classical Many-Body Problems Amenable to Exact Treatments (2001), Springer-Verlag: Springer-Verlag Berlin This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.