Citation: |
[1] |
D. Bothe, J. Prüss, $L_p$-theory for a class of non-Newtonian fluids, SIAM J. Math. Anal., 39 (2007), 379-421.doi: 10.1137/060663635. |
[2] |
D. M. Anderson, P. Cermelli, E. Fried, M. E. Gurtin and G. B. McFadden, General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids, J. Fluid Mech., 581 (2007), 323-370.doi: 10.1017/S0022112007005587. |
[3] |
E. DiBenedetto and A. Friedman, Conduction-convection problems with change of phase, J. Differential Equations, 62 (1986), 129-185. |
[4] |
E. DiBenedetto and M. O'Leary, Three-dimensional conduction-convection problems with change of phase, Arch. Rational Mech. Anal., 123 (1993), 99-116.doi: 10.1007/BF00695273. |
[5] |
R. Denk, M. Hieber and J. Prüss, "$\mathcal R$-boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type," AMS Memoirs, 788, Providence, R.I., 2003. |
[6] |
R. Denk, M. Hieber and J. Prüss, Optimal $L^ p$-$L^ q$-estimates for parabolic boundary value problems with inhomogeneous data, Math. Z., 257 (2007), 193-224.doi: 10.1007/s00209-007-0120-9. |
[7] |
K.-H. Hoffmann and V. N. Starovoitov, The Stefan problem with surface tension and convection in Stokes fluid, Adv. Math. Sci. Appl., 8 (1998), 173-183. |
[8] |
K.-H. Hoffmann and V. N. Starovoitov, Phase transitions of liquid-liquid type with convection, Adv. Math. Sci. Appl., 8 (1998), 185-198. |
[9] |
M. Ishii, "Thermo-Fluid Dynamics of Two-Phase Flow," Collection de la Direction des Etudes et Recherches d'Electricte de France, Paris, 1975. |
[10] |
M. Ishii and H. Takashi, "Thermo-Fluid Dynamics of Two-Phase Flow," Springer, New York, 2006. |
[11] |
M. Köhne, J. Prüss and M. Wilke, Qualitative behaviour of solutions for the two-phase Navier-Stokes equations with surface tension, Math. Annalen, to appear. |
[12] |
Y. Kusaka, On a limit problem of the Stefan problem with surface tension in a viscous incompressible fluid flow, Adv. Math. Sci. Appl., 12 (2002), 665-683. |
[13] |
Y. Kusaka and A. Tani, On the classical solvability of the Stefan problem in a viscous incompressible fluid flow, SIAM J. Math. Anal., 30 (1999), 584-602 (electronic).doi: 10.1137/S0036141098334936. |
[14] |
Y. Kusaka and A. Tani, Classical solvability of the two-phase Stefan problem in a viscous incompressible fluid flow, Math. Models Methods Appl. Sci., 12 (2002), 365-391.doi: 10.1142/S0218202502001696. |
[15] |
M. Meyries and R. Schnaubelt, Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions, Math. Nachr., to appear. |
[16] |
J. Prüss, Maximal regularity for evolution equations in $L_p$-spacess, Conf. Sem. Mat. Univ. Bari, 285 (2003), 1-39. |
[17] |
J. Prüss and S. Shimizu, Incompressible two-phase flows with phase transition: Non-equal densities, submitted. |
[18] |
J. Prüss and G. Simonett, Maximal regularity for evolution equations in weighted $L_p$-spaces, Archiv Math., 82 (2004), 415-431. |
[19] |
J. Prüss and G. Simonett, Stability of equilibria for the Stefan problem with surface tension, SIAM J. Math. Anal., 40 (2008), 675-698.doi: 10.1137/070700632. |
[20] |
J. Prüss and G. Simonett, On the two-phase Navier-Stokes equations with surface tension, Interfaces & Free Bound, 12 (2010), 311-345. |
[21] |
J. Prüss and G. Simonett, Analytic solutions for the two-phase Navier-Stokes equations with surface tension, Progr. Nonlin. Diff. Eqns. Appl., 80 (2011), 507-540. |
[22] |
J. Prüss, G. Simonett and R. Zacher, Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension, arXiv:1101.3763, submitted. |
[23] |
Y. Shibata and S. Shimizu, Resolvent estimates and maximal regularity of the interface problem for the Stokes system in a bounded domain, preprint, 2009. |
[24] |
N. Tanaka, Two-phase free boundary problem for viscous incompressible thermo-capillary convection, Japan J. Mech., 21 (1995), 1-41. |
[25] |
H. Triebel, "Theory of Function Spaces II," Birkhäuser Verlag, Basel, 1992. |