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 (2009)
- Volume: 26, Issue: 6, page 2403-2424
- ISSN: 0294-1449
Access Full Article
topHow to cite
topAbels, Helmut, and 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 26.6 (2009): 2403-2424. <http://eudml.org/doc/78940>.
@article{Abels2009,
author = {Abels, Helmut, Röger, Matthias},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {two-phase flow; Navier-Stokes equations; free boundary problems; Mullins-Sekerka system},
language = {eng},
number = {6},
pages = {2403-2424},
publisher = {Elsevier},
title = {Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids},
url = {http://eudml.org/doc/78940},
volume = {26},
year = {2009},
}
TY - JOUR
AU - Abels, Helmut
AU - Röger, Matthias
TI - Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2403
EP - 2424
LA - eng
KW - two-phase flow; Navier-Stokes equations; free boundary problems; Mullins-Sekerka system
UR - http://eudml.org/doc/78940
ER -
References
top- [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. Zbl1254.76158MR2563636
- [2] Abels H., On generalized solutions of two-phase flows for viscous incompressible fluids, Interfaces Free Bound.9 (2007) 31-65. Zbl1124.35060MR2317298
- [3] Abels H., On the notion of generalized solutions of two-phase flows for viscous incompressible fluids, RIMS Kôkyûroku BessatsuB1 (2007) 1-15. MR2312912
- [4] Ambrosio L., Fusco N., Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Clarendon Press, Oxford, 2000, xviii, p. 434. Zbl0957.49001MR1857292
- [5] Boyer F., Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptot. Anal.20 (2) (1999) 175-212. Zbl0937.35123MR1700669
- [6] Chen X., Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom.44 (2) (1996) 262-311. Zbl0874.35045MR1425577
- [7] Denisova I.V., Solonnikov V.A., 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. Zbl0756.35067MR1111467
- [8] Edwards R.E., Functional Analysis, Dover Publications, Inc., New York, 1995, 783 p. Zbl0182.16101MR1320261
- [9] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992. Zbl0804.28001MR1158660
- [10] Gurtin M.E., Polignone D., Viñals J., Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci.6 (6) (1996) 815-831. Zbl0857.76008MR1404829
- [11] Hoffmann K.-H., Starovoitov V.N., Phase transitions of liquid–liquid type with convection, Adv. Math. Sci. Appl.8 (1) (1998) 185-198. Zbl0958.35152MR1623346
- [12] Hohenberg P., Halperin B., Theory of dynamic critical phenomena, Rev. Modern Phys.49 (1977) 435-479.
- [13] Kim N., Consiglieri L., Rodrigues J.F., On non-Newtonian incompressible fluids with phase transitions, Math. Methods Appl. Sci.29 (13) (2006) 1523-1541. Zbl1101.76004MR2249576
- [14] Liu C., Shen J., A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method, Phys. D179 (3–4) (2003) 211-228. Zbl1092.76069MR1984386
- [15] Luckhaus S., Sturzenhecker T., Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations3 (2) (1995) 253-271. Zbl0821.35003MR1386964
- [16] Maekawa Y., On a free boundary problem for viscous incompressible flows, Interfaces Free Bound.9 (4) (2007) 549-589. Zbl1132.76303MR2358216
- [17] Modica L., The gradient theory of phase transitions and the minimal interface criterion, Arch. Ration. Mech. Anal.98 (2) (1987) 123-142. Zbl0616.76004MR866718
- [18] Modica L., Mortola S., Un esempio di -convergenza, Boll. Unione Mat. Ital. B (5)14 (1) (1977) 285-299. Zbl0356.49008MR445362
- [19] Plotnikov P., Generalized solutions to a free boundary problem of motion of a non-Newtonian fluid, Siberian Math. J.34 (4) (1993) 704-716. Zbl0814.76007MR1248797
- [20] Röger M., Solutions for the Stefan problem with Gibbs–Thomson law by a local minimisation, Interfaces Free Bound.6 (1) (2004) 105-133. Zbl1050.35155MR2047075
- [21] Schätzle R., Hypersurfaces with mean curvature given by an ambient Sobolev function, J. Differential Geom.58 (3) (2001) 371-420. Zbl1055.49032MR1906780
- [22] Simon J., Compact sets in the space , Ann. Mat. Pura Appl. (4)146 (1987) 65-96. Zbl0629.46031MR916688
- [23] Simon L., 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. Zbl0546.49019MR756417
- [24] Sohr H., The Navier–Stokes equations, in: Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Verlag, Basel, 2001, an elementary functional analytic approach. Zbl0983.35004MR1928881
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.