메뉴 건너뛰기




Volumn 76, Issue 1, 2013, Pages 1-13

Thin-film approximations of the two-phase Stokes problem

Author keywords

Degenerate parabolic system; Exponential stability; Strong solution; Thin film

Indexed keywords

DENSE FLUID; DENSE LAYER; EVOLUTION PROBLEM; GRAVITY DRIVEN FLOW; LAYER THICKNESS; PARABOLIC SYSTEM; STOKES PROBLEM; STRONG SOLUTION; STRONGLY COUPLED PARABOLIC SYSTEMS; TWO-FLUID;

EID: 84867051949     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2012.07.034     Document Type: Article
Times cited : (14)

References (28)
  • 2
    • 52049122591 scopus 로고    scopus 로고
    • A justification for the thin film approximation of Stokes flow with surface tension
    • M. Günther, and G. Prokert A justification for the thin film approximation of Stokes flow with surface tension J. Differential Equations 245 10 2008 2802 2845
    • (2008) J. Differential Equations , vol.245 , Issue.10 , pp. 2802-2845
    • Günther, M.1    Prokert, G.2
  • 3
    • 84865233521 scopus 로고    scopus 로고
    • Hele-Shaw flow in thin threads: A rigorous limit result
    • B.-V. Matioc, and G. Prokert Hele-Shaw flow in thin threads: a rigorous limit result Interfaces Free Bound. 14 2 2012 205 230
    • (2012) Interfaces Free Bound. , vol.14 , Issue.2 , pp. 205-230
    • Matioc, B.-V.1    Prokert, G.2
  • 4
    • 21144433755 scopus 로고    scopus 로고
    • Rigurous lubrication approximation
    • L. Giacomelli, and F. Otto Rigurous lubrication approximation Interfaces Free Bound. 5 4 2003 483 529
    • (2003) Interfaces Free Bound. , vol.5 , Issue.4 , pp. 483-529
    • Giacomelli, L.1    Otto, F.2
  • 5
    • 20444474618 scopus 로고    scopus 로고
    • Some aspects of the thin film equation
    • Barcelona, 2000 Procedings of European Congress of Mathematics Birkhäuser Verlag
    • J. Hulshof Some aspects of the thin film equation European Congress of Mathematics, Vol. II Barcelona, 2000 Procedings of European Congress of Mathematics vol. II 2001 Birkhäuser Verlag 291 301
    • (2001) European Congress of Mathematics, Vol. II , vol.2 , pp. 291-301
    • Hulshof, J.1
  • 7
    • 0041033033 scopus 로고
    • Two fluid systems in porous media. The encroachment of water into an oil sand
    • M. Muskat Two fluid systems in porous media. The encroachment of water into an oil sand Physics 5 1934 250 264
    • (1934) Physics , vol.5 , pp. 250-264
    • Muskat, M.1
  • 9
    • 79960623276 scopus 로고    scopus 로고
    • Modelling and analysis of the Muskat problem for thin fluid layers
    • J. Escher, A.-V. Matioc, and B.-V. Matioc Modelling and analysis of the Muskat problem for thin fluid layers J. Math. Fluid Mech. 14 2012 267 277
    • (2012) J. Math. Fluid Mech. , vol.14 , pp. 267-277
    • Escher, J.1    Matioc, A.-V.2    Matioc, B.-V.3
  • 10
    • 84878411593 scopus 로고    scopus 로고
    • Existence and stability of solutions for a strongly coupled system modelling thin fluid films
    • 10.1007/s00030-012-0166-1
    • J. Escher, and B.-V. Matioc Existence and stability of solutions for a strongly coupled system modelling thin fluid films NoDEA Nonlinear Differential Equations Appl. 2012 10.1007/s00030-012-0166-1
    • (2012) NoDEA Nonlinear Differential Equations Appl.
    • Escher, J.1    Matioc, B.-V.2
  • 11
    • 84858405608 scopus 로고    scopus 로고
    • A generalized Rayleigh-Taylor condition for the Muskat problem
    • J. Escher, A.-V. Matioc, and B.-V. Matioc A generalized Rayleigh-Taylor condition for the Muskat problem Nonlinearity 25 2012 73 92
    • (2012) Nonlinearity , vol.25 , pp. 73-92
    • Escher, J.1    Matioc, A.-V.2    Matioc, B.-V.3
  • 12
    • 79960641120 scopus 로고    scopus 로고
    • Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media
    • J. Escher, Ph. Laurençot, and B.-V. Matioc Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media Ann. Inst. H. Poincaré Anal. Non Linéaire 28 4 2011 583 598
    • (2011) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.28 , Issue.4 , pp. 583-598
    • Escher, J.1    Laurençot, Ph.2    Matioc, B.-V.3
  • 13
    • 84869997056 scopus 로고    scopus 로고
    • Nonnegative global weak solutions for a degenerate parabolic system modeling thin films driven by capillarity
    • (in press)
    • B.-V. Matioc, Nonnegative global weak solutions for a degenerate parabolic system modeling thin films driven by capillarity, Proc. Roy. Soc. Edinburgh Sect. A (2012) (in press).
    • (2012) Proc. Roy. Soc. Edinburgh Sect. A
    • Matioc, B.-V.1
  • 14
    • 84876434103 scopus 로고    scopus 로고
    • A gradient flow approach to a thin film approximation of the Muskat problem
    • 10.1007/s00526-012-0520-5
    • Ph. Laurençot, and B.-V. Matioc A gradient flow approach to a thin film approximation of the Muskat problem Calc. Var. Partial Differential Equations 2012 10.1007/s00526-012-0520-5
    • (2012) Calc. Var. Partial Differential Equations
    • Laurençot, Ph.1    Matioc, B.-V.2
  • 15
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto The geometry of dissipative evolution equations: the porous medium equation Comm. Partial Differential Equations 26 1-2 2001 101 174
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.12 , pp. 101-174
    • Otto, F.1
  • 16
    • 33645123673 scopus 로고    scopus 로고
    • Analyticity of solutions to nonlinear parabolic equations on manifolds and an application to Stokes flow
    • J. Escher, and G. Prokert Analyticity of solutions to nonlinear parabolic equations on manifolds and an application to Stokes flow J. Math. Fluid Mech. 8 1 2006 1 35
    • (2006) J. Math. Fluid Mech. , vol.8 , Issue.1 , pp. 1-35
    • Escher, J.1    Prokert, G.2
  • 17
    • 0037059123 scopus 로고    scopus 로고
    • Quasi-static motion of a capillary drop. II. The three-dimensional case
    • A. Friedman, and F. Reitich Quasi-static motion of a capillary drop. II. The three-dimensional case J. Differential Equations 186 2 2002 509 557
    • (2002) J. Differential Equations , vol.186 , Issue.2 , pp. 509-557
    • Friedman, A.1    Reitich, F.2
  • 18
    • 0036158028 scopus 로고    scopus 로고
    • Quasistatic motion of a capillary drop. I. The two-dimensional case
    • A. Friedman, and F. Reitich Quasistatic motion of a capillary drop. I. The two-dimensional case J. Differential Equations 178 1 2002 212 263
    • (2002) J. Differential Equations , vol.178 , Issue.1 , pp. 212-263
    • Friedman, A.1    Reitich, F.2
  • 19
    • 0001831250 scopus 로고    scopus 로고
    • On quasistationary approximation in the problem of motion of a capillary drop
    • Progr. Nonlinear Differential Equations Appl. Birkhäuser Basel
    • V.A. Solonnikov On quasistationary approximation in the problem of motion of a capillary drop Topics in Nonlinear Analysis Progr. Nonlinear Differential Equations Appl. vol. 35 1999 Birkhäuser Basel 643 671
    • (1999) Topics in Nonlinear Analysis , vol.35 , pp. 643-671
    • Solonnikov, V.A.1
  • 20
    • 84879409996 scopus 로고    scopus 로고
    • On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations with surface tension
    • (in press)
    • J. Prüss, G. Simonett, On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations with surface tension, Indiana Univ. Math. J. (in press).
    • Indiana Univ. Math. J.
    • J. Prüss1
  • 21
    • 77958031714 scopus 로고    scopus 로고
    • On the two-phase Navier-Stokes equations with surface tension
    • J. Prüss, and G. Simonett On the two-phase Navier-Stokes equations with surface tension Interfaces Free Bound. 12 3 2010 311 345
    • (2010) Interfaces Free Bound. , vol.12 , Issue.3 , pp. 311-345
    • Prüss, J.1    Simonett, G.2
  • 22
    • 85016600894 scopus 로고    scopus 로고
    • Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity
    • Progr. Nonlinear Differential Equations Appl. Birkhäuser Basel
    • J. Prüss, and G. Simonett Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity Parabolic Problems. The Herbert Amann Festschrift Progr. Nonlinear Differential Equations Appl. vol. 80 2011 Birkhäuser Basel 507 580
    • (2011) Parabolic Problems. The Herbert Amann Festschrift , vol.80 , pp. 507-580
    • Prüss, J.1    Simonett, G.2
  • 24
    • 0001835099 scopus 로고
    • Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
    • Teubner-Texte Math. Teubner Stuttgart
    • H. Amann Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems Function Spaces, Differential Operators and Nonlinear Analysis Teubner-Texte Math. vol. 133 1993 Teubner Stuttgart 9 126
    • (1993) Function Spaces, Differential Operators and Nonlinear Analysis , vol.133 , pp. 9-126
    • Amann, H.1
  • 25
    • 84856449541 scopus 로고    scopus 로고
    • Thin film equations with soluble surfactant and gravity: Modeling and stability of steady states
    • J. Escher, Ch. Walker, Ph. Laurençot, and M. Hillairet Thin film equations with soluble surfactant and gravity: modeling and stability of steady states Math. Nachr. 285 2-3 2012 210 222
    • (2012) Math. Nachr. , vol.285 , Issue.23 , pp. 210-222
    • Escher, J.1    Walker, Ch.2    Laurençot, Ph.3    Hillairet, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.