Kusaka, Yoshiaki Classical solvability of a free boundary problem for an incompressible viscous fluid with a surface density equation. (English) Zbl 1292.35342 Abstr. Appl. Anal. 2013, Article ID 495408, 9 p. (2013). Summary: We investigate a mathematical model introduced by Shikhmurzaev to remove singularities that arise when classical hydrodynamic models are applied to certain physical phenomena. The model is described as a free boundary problem consisting of the Navier-Stokes equations and a surface mass balance equation. We prove the local-in-time solvability in Hölder spaces. Cited in 2 Documents MSC: 35R35 Free boundary problems for PDEs 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:free boundary problem; incompressible viscous fluid; Navier-Stokes equations; surface mass balance equation; local-in-time solvability; Hölder spaces × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Shikhmurzaev, Y. D., Capillary Flows with Forming Interfaces, xx+456 (2008), Boca Raton, Fla, USA: Chapman & Hall/CRC, Boca Raton, Fla, USA · Zbl 1165.76001 [2] Shikhmurzaev, Y. D., The moving contact line on a smooth solid surface, International Journal of Multiphase Flow, 19, 4, 589-610 (1993) · Zbl 1144.76452 [3] Shikhmurzaev, Y. D., Moving contact lines in liquid/liquid/solid systems, Journal of Fluid Mechanics, 334, 211-249 (1997) · Zbl 0887.76021 · doi:10.1017/S0022112096004569 [4] Shikhmurzaev, Y. D., On cusped interfaces, Journal of Fluid Mechanics, 359, 313-328 (1998) · Zbl 0914.76029 · doi:10.1017/S0022112098008532 [5] Wong, H.; Rumschitzki, D.; Maldarelli, C., On the surfactant mass balance at a deforming fluid interface, Physics of Fluids, 8, 11, 3203-3204 (1996) · Zbl 1027.76667 [6] Mogilevskiĭ, I. Sh.; Solonnikov, V. A., On the solvability of an evolution free boundary problem for the Navier-Stokes equations in Hölder spaces of functions, Mathematical Problems Relating to the Navier-Stokes Equation. Mathematical Problems Relating to the Navier-Stokes Equation, Advances in Mathematics for Applied Sciences, 11, 105-181 (1992), River Edge, NJ, USA: World Science Publications, River Edge, NJ, USA · Zbl 0793.35072 [7] Lady ženskaja, O. A.; Solonnikov, V. A.; Ural’ceva, N. N., Linear and quasi-linear equations of parabolic type, Translations of Mathematical Monographs (1968) · Zbl 0174.15403 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.