@article{AIHPC_2009__26_6_2403_0, author = {Abels, Helmut and R\"oGer, Matthias}, title = {Existence of Weak Solutions for a Non-Classical Sharp Interface Model for a Two-Phase Flow of Viscous, Incompressible Fluids}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {26}, year = {2009}, pages = {2403-2424}, doi = {10.1016/j.anihpc.2009.06.002}, mrnumber = {2569901}, zbl = {pre05649879}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2403_0} }
Abels, Helmut; RöGer, Matthias. Existence of Weak Solutions for a Non-Classical Sharp Interface Model for a Two-Phase Flow of Viscous, Incompressible Fluids. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2403-2424. doi : 10.1016/j.anihpc.2009.06.002. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2403_0/
[1] H. Abels, On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities, Arch. Rat. Mech. Anal., doi:10.1007/s00205-008-0160-2. | MR 2563636 | Zbl pre05640833
[2] On Generalized Solutions of Two-Phase Flows for Viscous Incompressible Fluids, Interfaces Free Bound. 9 (2007) 31-65. | MR 2317298 | Zbl 1124.35060
,[3] On the Notion of Generalized Solutions of Two-Phase Flows for Viscous Incompressible Fluids, RIMS Kôkyûroku Bessatsu B1 (2007) 1-15. | MR 2312912 | Zbl 1119.35042
,[4] Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Clarendon Press, Oxford, 2000, xviii, p. 434. | MR 1857292 | Zbl 0957.49001
, , ,[5] Mathematical Study of Multi-Phase Flow Under Shear Through Order Parameter Formulation, Asymptot. Anal. 20 (2) (1999) 175-212. | MR 1700669 | Zbl 0937.35123
,[6] Global Asymptotic Limit of Solutions of the Cahn-Hilliard Equation, J. Differential Geom. 44 (2) (1996) 262-311. | MR 1425577 | Zbl 0874.35045
,[7] Solvability in Hölder Spaces of a Model Initial-Boundary Value Problem Generated by a Problem on the Motion of Two Fluids, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 188 (1991) 5-44, Funktsii. Kraev. Zadachi Mat. Fiz. i Smezh. Voprosy Teor. 22 (1991) 5-44, 186. | MR 1111467 | Zbl 0756.35067
, ,[8] Functional Analysis, Dover Publications, Inc., New York, 1995, 783 p. | MR 1320261 | Zbl 0182.16101
,[9] Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992. | MR 1158660 | Zbl 0804.28001
, ,[10] Two-Phase Binary Fluids and Immiscible Fluids Described by an Order Parameter, Math. Models Methods Appl. Sci. 6 (6) (1996) 815-831. | MR 1404829 | Zbl 0857.76008
, , ,[11] Phase Transitions of Liquid-Liquid Type With Convection, Adv. Math. Sci. Appl. 8 (1) (1998) 185-198. | MR 1623346 | Zbl 0958.35152
, ,[12] Theory of Dynamic Critical Phenomena, Rev. Modern Phys. 49 (1977) 435-479.
, ,[13] On Non-Newtonian Incompressible Fluids With Phase Transitions, Math. Methods Appl. Sci. 29 (13) (2006) 1523-1541. | MR 2249576 | Zbl 1101.76004
, , ,[14] A Phase Field Model for the Mixture of Two Incompressible Fluids and Its Approximation by a Fourier-Spectral Method, Phys. D 179 (3-4) (2003) 211-228. | MR 1984386 | Zbl 1092.76069
, ,[15] Implicit Time Discretization for the Mean Curvature Flow Equation, Calc. Var. Partial Differential Equations 3 (2) (1995) 253-271. | MR 1386964 | Zbl 0821.35003
, ,[16] On a Free Boundary Problem for Viscous Incompressible Flows, Interfaces Free Bound. 9 (4) (2007) 549-589. | MR 2358216 | Zbl 1132.76303
,[17] The Gradient Theory of Phase Transitions and the Minimal Interface Criterion, Arch. Ration. Mech. Anal. 98 (2) (1987) 123-142. | MR 866718 | Zbl 0616.76004
,[18] Un Esempio Di -Convergenza, Boll. Unione Mat. Ital. B (5) 14 (1) (1977) 285-299. | MR 445362 | Zbl 0356.49008
, ,[19] Generalized Solutions to a Free Boundary Problem of Motion of a Non-Newtonian Fluid, Siberian Math. J. 34 (4) (1993) 704-716. | MR 1248797 | Zbl 0814.76007
,[20] Solutions for the Stefan Problem With Gibbs-Thomson Law by a Local Minimisation, Interfaces Free Bound. 6 (1) (2004) 105-133. | MR 2047075 | Zbl 1050.35155
,[21] Hypersurfaces With Mean Curvature Given by an Ambient Sobolev Function, J. Differential Geom. 58 (3) (2001) 371-420. | MR 1906780 | Zbl 1055.49032
,[22] Compact Sets in the Space , Ann. Mat. Pura Appl. (4) 146 (1987) 65-96. | MR 916688 | Zbl 0629.46031
,[23] Lectures on Geometric Measure Theory, Vol. 3, in: Proceedings of the Centre for Mathematical Analysis, Australian National University, Australian National University Centre for Mathematical Analysis, Canberra, 1983. | MR 756417 | Zbl 0546.49019
,[24] The Navier-Stokes Equations, in: Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Verlag, Basel, 2001, an elementary functional analytic approach. | MR 1928881 | Zbl 0983.35004
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