References
V. I. Nalimov, “A priori estimates for solutions to elliptic equations in the class of analytic functions and their applications to the Cauchy-Poisson problem,” Dokl. Akad. Nauk SSSR,189, No. 1, 45–49 (1969).
L. V. Ovsjannikov, “Nonlocal Cauchy problems in fluid dynamics,” Actes du Congres International des Mathematiciens, No. 3, Gauthier-Villars, Paris (1971).
M. Shinbrot, “The initial value problem for surface waves under gravity. I: The simplest case,” Indiana Univ. Math. J.,25, No. 3, 281–300 (1976).
V. I. Nalimov, “The Cauchy-Poisson problem,” Dinamika Sploshn. Sredy (Novosibirsk),18, 104–210 (1974).
M. Yoshihara, “Gravity waves on the free surface of an incompressible perfect fluid of finite depth,” Kyoto Univ. Math. J,18, 49–96 (1982).
V. I. Nalimov, “Justification of approximate models of the theory of plane unsteady waves,” in: Nonlocal Problems in the Theory of Surface and Internal Waves [in Russian], Nauka, Novosibirsk, 1985, pp. 97–127.
M. A. Bimenov, “The space Cauchy-Poisson problem in classes of functions with finite smoothness,” Dinamika Sploshn. Sredy (Novosibirsk),109, 65–78 (1994).
V. I. Nalimov, “A model problem of vertical surface waves,” Sibirsk. Mat. Zh.,35, No. 5, 1119–1124 (1994).
J. J. Stoker, Water Waves. Mathematical Theory and Applications [Russian translation], Izdat. Inostr. Lit., Moscow (1959).
J.-L. Lions and E. Magenes, Problémes aux Limites Non Homogénes et Applications. Vol. 1 [Russian translation], Mir, Moscow (1971).
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The research is financially supported by the Russian Foundation for Basic Research (Grant 93-013-17621).
Translated from Sibirskii Matematicheskii, Vol. 37, No. 6, pp. 1356–1366, November–December, 1996.
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Nalimov, V.I. Nonstationary vortex surface waves. Sib Math J 37, 1189–1198 (1996). https://doi.org/10.1007/BF02106744
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DOI: https://doi.org/10.1007/BF02106744