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Analyticity for the Navier-Stokes equations governed by surface tension on the free boundary. (English) Zbl 0497.35076


MSC:

35Q30 Navier-Stokes equations
35R30 Inverse problems for PDEs
35B65 Smoothness and regularity of solutions to PDEs
35B45 A priori estimates in context of PDEs
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[1] Agmon, S.; Douglis, J.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. Pure Appl. Math., 17, 35-92 (1964) · Zbl 0123.28706
[2] Bemelmans, J., Gleichgewichtsfiguren zäher Flussigkeiten unter dem Einfluss von Oberflächenspannung, Analysis, 1 (1981) · Zbl 0561.76042
[3] Bemelmans, J., Liquid drops in a viscous fluid under the influence of gravity and surface tension, Manuscripta Math., 36, 105-123 (1981) · Zbl 0478.76118
[5] Friedman, A., On the regularity of solutions of nonlinear elliptic and parabolic systems of partial differential equations, J. Math. Mech., 7, 43-60 (1958) · Zbl 0078.27702
[6] Isakov, V. M., Inverse theorems concerning the smoothness of potentials, J. Differential Equations, 11, 50-56 (1974), (translated from Russian) · Zbl 0328.31010
[7] Isakov, V. M., Analyticity of solutions of nonlinear transmission problems, J. Differential Equations, 12, 41-47 (1976), (translated from Russian) · Zbl 0343.35035
[8] Kinderlehrer, D.; Nirenberg, L., Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa, 4, 373-391 (1977), (4) · Zbl 0352.35023
[9] Kinderlehrer, D.; Nirenberg, L.; Spruck, J., Regularity in elliptic free boundary problems, I, J. Analyse Math., 34, 86-119 (1978) · Zbl 0402.35045
[10] Kinderlehrer, D.; Nirenberg, L.; Spruck, J., Regularity in elliptic free boundary problems. II. Equations of higher order, Ann. Scuola Norm. Sup. Pisa, 6, 637-683 (1979), (4) · Zbl 0425.35097
[11] Morrey, C. B., On the analyticity of solutions of analytic non-linear elliptic systems of partial differential equations, I and II, Amer. J. Math., 80, 198-237 (1958) · Zbl 0081.09402
[12] Morrey, C. B., Multiple Integrals in the Calculus of Variations (1966), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0142.38701
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