Movatterモバイル変換

[0]ホーム
URL:

×

zbMATH Open — the first resource for mathematics

from until
Reset all

Examples

GeometrySearch for the termGeometry inany field. Queries arecase-independent.
Funct*Wildcard queries are specified by* (e .g.functions,functorial, etc.). Otherwise the search isexact.''Topological group'':Phrases (multi - words) should be set in''straight quotation marks''.
au: Bourbaki & ti: AlgebraSearch forauthorBourbaki andtitleAlgebra. Theand-operator & is default and can be omitted.
Chebyshev | TschebyscheffTheor-operator| allows to search forChebyshev orTschebyscheff.
Quasi* map* py: 1989The resulting documents havepublicationyear1989.
so:Eur* J* Mat* Soc* cc:14Search for publications in a particularsource with aMathematics SubjectClassificationcode in14.
cc:*35 ! any:ellipticSearch for documents about PDEs (prefix with * to search only primary MSC); the not-operator ! eliminates all results containing the wordelliptic.
dt: b & au: HilbertThedocumenttype is set tobooks; alternatively:j forjournal articles,a forbookarticles.
py: 2000 - 2015 cc:(94A | 11T)Numberranges when searching forpublicationyear are accepted . Terms can be grouped within( parentheses).
la: chineseFind documents in a givenlanguage .ISO 639 - 1 (opens in new tab) language codes can also be used.
st: c r sFind documents that arecited, havereferences and are from asingle author.

Fields

ab Text from the summary or review (for phrases use “. ..”)
an zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number
any Includes ab, au, cc, en, rv, so, ti, ut
arxiv arXiv preprint number
au Name(s) of the contributor(s)
br Name of a person with biographic references (to find documents about the life or work)
cc Code from the Mathematics Subject Classification (prefix with* to search only primary MSC)
ci zbMATH ID of a document cited in summary or review
db Database: documents in Zentralblatt für Mathematik/zbMATH Open (db:Zbl), Jahrbuch über die Fortschritte der Mathematik (db:JFM), Crelle's Journal (db:eram), arXiv (db:arxiv)
dt Type of the document: journal article (dt:j), collection article (dt:a), book (dt:b)
doi Digital Object Identifier (DOI)
ed Name of the editor of a book or special issue
en External document ID: DOI, arXiv ID, ISBN, and others
in zbMATH ID of the corresponding issue
la Language (use name, e.g.,la:French, orISO 639-1, e.g.,la:FR)
li External link (URL)
na Number of authors of the document in question. Interval search with “-”
pt Reviewing state: Reviewed (pt:r), Title Only (pt:t), Pending (pt:p), Scanned Review (pt:s)
pu Name of the publisher
py Year of publication. Interval search with “-”
rft Text from the references of a document (for phrases use “...”)
rn Reviewer ID
rv Name or ID of the reviewer
se Serial ID
si swMATH ID of software referred to in a document
so Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc.
st State: is cited (st:c), has references (st:r), has single author (st:s)
sw Name of software referred to in a document
ti Title of the document
ut Keywords

Operators

a & bLogical and (default)
a | bLogical or
!abLogical not
abc*Right wildcard
ab cPhrase
(ab c)Term grouping

See also ourGeneral Help.

Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities.(English)Zbl 1273.76421

Summary: We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed byH. Abels et al. [Math. Models Methods Appl. Sci. 22, No. 3, 1150013, 40 p. (2012;Zbl 1242.76342)] for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter.

MSC:

76T99 Multiphase and multicomponent flows
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D27 Other free boundary flows; Hele-Shaw flows
76D45 Capillarity (surface tension) for incompressible viscous fluids

Citations:

Zbl 1242.76342

Cite

References:

[1]Abels, H.: Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids. Habilitation Thesis, Leipzig (2007) ·Zbl 1124.35060
[2]Abels H.: Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities. Comm. Math. Phys. 289, 45-73 (2009) ·Zbl 1165.76050 ·doi:10.1007/s00220-009-0806-4
[3]Abels H.: On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities. Arch. Rat. Mech. Anal. 194, 463-506 (2009) ·Zbl 1254.76158 ·doi:10.1007/s00205-008-0160-2
[4]Abels H.: Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow. SIAM J. Math. Anal. 44(1), 316-340 (2012) ·Zbl 1333.76079 ·doi:10.1137/110829246
[5]Abels, H., Garcke, H., Grün, G.: Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities. preprint Nr. 20/2010 University Regensburg (2010) ·Zbl 1242.76342
[6]Abels H., Garcke H., Grün G.: Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Math. Models Meth. Appl. Sci. 22(3), 1150013 (2011) ·Zbl 1242.76342 ·doi:10.1142/S0218202511500138
[7]Abels H., Röger M.: Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 26(6), 2403-2424 (2009) ·Zbl 1181.35343 ·doi:10.1016/j.anihpc.2009.06.002
[8]Abels H., Wilke M.: Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy. Nonlin. Anal. 67, 3176-3193 (2007) ·Zbl 1121.35018 ·doi:10.1016/j.na.2006.10.002
[9]Amann H.: Linear and Quasilinear Parabolic Problems, vol. 1: Abstract Linear Theory. Birkhäuser, Basel (1995) ·Zbl 0819.35001 ·doi:10.1007/978-3-0348-9221-6
[10]Anderson, D.-M., McFadden, G.B., Wheeler, A.A.: Diffuse interface methods in fluid mechanics. Annu. Rev. Fluid Mech., vol. 30, pp. 139-165. Annual Reviews, Paolo Alto (1998) ·Zbl 1398.76051
[11]Bergh J., Löfström J.: Interpolation Spaces. Springer, Berlin (1976) ·Zbl 0344.46071 ·doi:10.1007/978-3-642-66451-9
[12]Boyer F.: Mathematical study of multi-phase flow under shear through order parameter formulation. Asymptot. Anal. 20(2), 175-212 (1999) ·Zbl 0937.35123
[13]Boyer F.: Nonhomogeneous Cahn-Hilliard fluids. Ann. Inst. H. Poincar Anal. Non Linaire 18(2), 225-259 (2001) ·Zbl 1037.76062 ·doi:10.1016/S0294-1449(00)00063-9
[14]Cahn J.W., Hilliard J.E.: Free energy of a nonuniform system. I. Interfacial energy. J. Chem. Phys. 28(2), 258-267 (1958) ·Zbl 1431.35066 ·doi:10.1063/1.1744102
[15]Diestel, J., Uhl, J.J., Jr.: Vector Measures. Am. Math. Soc., Providence (1977) ·Zbl 0369.46039
[16]Ding H., Spelt P.D.M., Shu C.: Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comp. Phys. 22, 2078-2095 (2007) ·Zbl 1388.76403 ·doi:10.1016/j.jcp.2007.06.028
[17]Gurtin M.E., Polignone D., Viñals J.: Two-phase binary fluids and immiscible fluids described by an order parameter. Math. Models Meth. Appl. Sci. 6(6), 815-831 (1996) ·Zbl 0857.76008 ·doi:10.1142/S0218202596000341
[18]Hohenberg P.C., Halperin B.I.: Theory of dynamic critical phenomena. Rev. Mod. Phys. 49, 435-479 (1977) ·doi:10.1103/RevModPhys.49.435
[19]Lions J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non linéaires. Dunod, Paris (1969) ·Zbl 0189.40603
[20]Lions P.-L.: Mathematical Topics in Fluid Mechanics, vol. 1, Incompressible Models. Clarendon Press, Oxford (1996) ·Zbl 0866.76002
[21]Liu C., Shen J.: A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Phys. D 179(3-4), 211-228 (2003) ·Zbl 1092.76069 ·doi:10.1016/S0167-2789(03)00030-7
[22]Lowengrub J., Truskinovsky L.: Quasi-incompressible Cahn-Hilliard fluids and topological transitions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454, 2617-2654 (1998) ·Zbl 0927.76007 ·doi:10.1098/rspa.1998.0273
[23]Roubíček T.: A generalization of the Lions-Temam compact embedding theorem. Časopis Pěst Mat. 115(4), 338-342 (1990) ·Zbl 0755.46013
[24]Showalter R.E.: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. AMS, Providence (1997) ·Zbl 0870.35004
[25]Simon J.: Compact sets in the space Lp(0,T;B). Ann. Mat. Pura Appl. 146(4), 65-96 (1987) ·Zbl 0629.46031
[26]Sohr, H.: The Navier-Stokes Equations. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser, Basel (2001) ·Zbl 0983.35004
[27]Starovoĭtov, V.N.: On the motion of a two-component fluid in the presence of capillary forces. Mat. Zametki 62(2), 293-305 (1997) transl. in Math. Notes, 62(1-2), 244-254 (1997) ·Zbl 0921.35134
[28]Stein E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970) ·Zbl 0207.13501
[29]Triebel H.: Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam (1978) ·Zbl 0387.46032
[30]Zeidler E.: Nonlinear Functional Analysis and its Applications I. Springer, New York (1992)
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.
© 2025FIZ Karlsruhe GmbHPrivacy PolicyLegal NoticesTerms & Conditions
  • Mastodon logo
 (opens in new tab)
[8]ページ先頭
©2009-2025 Movatter.jp