메뉴 건너뛰기




Volumn 12, Issue 3, 2010, Pages 311-345

On the two-phase Navier-Stokes equations with surface tension

Author keywords

Analyticity; Navier Stokes equations; Surface tension; Well posedness

Indexed keywords


EID: 77958031714     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/237     Document Type: Article
Times cited : (104)

References (58)
  • 1
    • 0023385699 scopus 로고
    • Small-time existence for the Navier-Stokes equations with a free surface
    • Zbl 0655.76021 MR 0883473
    • ALLAIN, G. Small-time existence for the Navier-Stokes equations with a free surface. Appl. Math. Optim. 16 (1987), 37-50. Zbl 0655.76021 MR 0883473
    • (1987) Appl. Math. Optim. , vol.16 , pp. 37-50
    • Allain, G.1
  • 3
    • 84974028928 scopus 로고
    • Nonlinear analytic semiflows
    • Zbl 0723.34047 MR 1059647
    • ANGENENT, S. Nonlinear analytic semiflows. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), 91-107. Zbl 0723.34047 MR 1059647
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 91-107
    • Angenent, S.1
  • 6
    • 0021197315 scopus 로고
    • Large-time regularity of viscous surface waves
    • Zbl 0545.76029 MR 0721189
    • BEALE, J. T. Large-time regularity of viscous surface waves. Arch. Ration. Mech. Anal. 84 (1983/84), 307-352. Zbl 0545.76029 MR 0721189
    • (1983) Arch. Ration. Mech. Anal. , vol.84 , pp. 307-352
    • Beale, J.T.1
  • 9
    • 41449103407 scopus 로고    scopus 로고
    • Lp-theory for a class of non-Newtonian fluids
    • Zbl 1172.35052 MR 2338412
    • BOTHE, D. & PRÜSS, J. Lp-theory for a class of non-Newtonian fluids. SIAM J. Math. Anal. 39 (2007), 379-421. Zbl 1172.35052 MR 2338412
    • (2007) SIAM J. Math. Anal. , vol.39 , pp. 379-421
    • Bothe, D.1    Prüss, J.2
  • 10
    • 52849095191 scopus 로고
    • A priori estimates for the solution of a linear nonstationary problem connected with the motion of a drop in a liquid medium
    • 3-21 (in Russian); English transl.
    • DENISOVA, I. V. A priori estimates for the solution of a linear nonstationary problem connected with the motion of a drop in a liquid medium. Trudy Mat. Inst. Steklov. 188 (1990), 3-21 (in Russian); English transl.
    • (1990) Trudy Mat. Inst. Steklov. , vol.188
    • Denisova, I.V.1
  • 11
    • 77958065691 scopus 로고
    • Zbl 0737.35063 MR 1100535
    • Proc. Steklov Inst. Math. 188 (1991), 1-24. Zbl 0737.35063 MR 1100535
    • (1991) Proc. Steklov Inst. Math. , vol.188 , pp. 1-24
  • 12
    • 34249767809 scopus 로고
    • Problem of the motion of two viscous incompressible fluids separated by a closed free interface. In: Mathematical Problems for Navier-Stokes Equations (Centro, 1993)
    • Zbl 0814.35093 MR 1308743
    • DENISOVA, I. V. Problem of the motion of two viscous incompressible fluids separated by a closed free interface. In: Mathematical Problems for Navier-Stokes Equations (Centro, 1993), Acta Appl. Math. 37 (1994), 31-40. Zbl 0814.35093 MR 1308743
    • (1994) Acta Appl. Math. , vol.37 , pp. 31-40
    • Denisova, I.V.1
  • 13
    • 0038413070 scopus 로고
    • Classical solvability of the problem of the motion of two viscous incompressible fluids
    • (in Russian); English transl.
    • DENISOVA, I. V., & SOLONNIKOV, V. A. Classical solvability of the problem of the motion of two viscous incompressible fluids. Algebra i Analiz 7 (1995), no. 5, 101-142 (in Russian); English transl.
    • (1995) Algebra i Analiz , vol.7 , Issue.5 , pp. 101-142
    • Denisova, I.V.1    Solonnikov, V.A.2
  • 14
    • 67349215347 scopus 로고    scopus 로고
    • Zbl 0859.35093 MR 1365814
    • St. Petersburg Math. J. 7 (1996), no. 5, 755-786. Zbl 0859.35093 MR 1365814
    • (1996) St. Petersburg Math. J. , vol.7 , Issue.5 , pp. 755-786
  • 15
    • 0242287337 scopus 로고    scopus 로고
    • R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type
    • Zbl pre02021354 MR 200664114
    • DENK, R., HIEBER, M., & PRÜSS, J. R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type. Mem. Amer. Math. Soc. 166 (2003), no. 788. Zbl pre02021354 MR 200664114.
    • (2003) Mem. Amer. Math. Soc. , vol.166 , Issue.788
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 16
    • 34250882162 scopus 로고    scopus 로고
    • q-estimates for parabolic boundary value problems with inhomogeneous data
    • Zbl pre05199467 MR 2318575
    • q-estimates for parabolic boundary value problems with inhomogeneous data. Math. Z. 257 (2007), 193-224. Zbl pre05199467 MR 2318575
    • (2007) Math. Z. , vol.257 , pp. 193-224
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 17
    • 0042851359 scopus 로고    scopus 로고
    • Lp-theory of the Stokes equation in a half space
    • Zbl 0983.35102 MR 1838323
    • DESCH, W., HIEBER, M., & PRÜSS, J. Lp-theory of the Stokes equation in a half space. J. Evol. Equations 1 (2001), 115-142. Zbl 0983.35102 MR 1838323
    • (2001) J. Evol. Equations , vol.1 , pp. 115-142
    • Desch, W.1    Hieber, M.2    Prüss, J.3
  • 18
    • 0037874989 scopus 로고
    • On the closedness of the sum of two closed operators
    • Zbl 0615.47002 MR 0910825
    • DORE, G., & VENNI, A. On the closedness of the sum of two closed operators. Math. Z. 196 (1987), 189-201. Zbl 0615.47002 MR 0910825
    • (1987) Math. Z. , vol.196 , pp. 189-201
    • Dore, G.1    Venni, A.2
  • 19
    • 0039470279 scopus 로고    scopus 로고
    • Analyticity of the interface in a free boundary problem
    • ESCHER, J., & SIMONETT, G. Analyticity of the interface in a free boundary problem. Math. Ann. 305 (1996), 439-459. Zbl 0857.76086 MR 1397432 (Pubitemid 126338933)
    • (1996) Mathematische Annalen , vol.305 , Issue.3 , pp. 439-459
    • Escher, J.1    Simonett, G.2
  • 20
    • 1642325884 scopus 로고    scopus 로고
    • Analyticity of solutions to fully nonlinear parabolic evolution equations on symmetric spaces
    • Zbl 1064.58011 MR 2058051
    • ESCHER, J., & SIMONETT, G. Analyticity of solutions to fully nonlinear parabolic evolution equations on symmetric spaces. J. Evol. Equations 3 (2003), 549-576. Zbl 1064.58011 MR 2058051
    • (2003) J. Evol. Equations , vol.3 , pp. 549-576
    • Escher, J.1    Simonett, G.2
  • 21
    • 0242338686 scopus 로고    scopus 로고
    • Analytic solutions for a Stefan problem with Gibbs-Thomson correction
    • Zbl pre02005574 MR 2009238
    • ESCHER, J., PRÜSS, J., & SIMONETT, G. Analytic solutions for a Stefan problem with Gibbs-Thomson correction. J. Reine Angew. Math. 563 (2003), 1-52. Zbl pre02005574 MR 2009238
    • (2003) J. Reine Angew. Math. , vol.563 , pp. 1-52
    • Escher, J.1    Prüss, J.2    Simonett, G.3
  • 22
    • 27844593328 scopus 로고    scopus 로고
    • A new approach to the regularity of solutions for parabolic equations
    • Dekker, New York. Zbl 1070.35009 MR 2073744
    • ESCHER, J., PRÜSS, J., & SIMONETT, G. A new approach to the regularity of solutions for parabolic equations. In: Evolution Equations, Lecture Notes in Pure Appl. Math. 234, Dekker, New York (2003), 167-190. Zbl 1070.35009 MR 2073744
    • (2003) Evolution Equations, Lecture Notes in Pure Appl. Math. , vol.234 , pp. 167-190
    • Escher, J.1    Prüss, J.2    Simonett, G.3
  • 24
    • 23944526313 scopus 로고    scopus 로고
    • H∞-calculus for products of non-commuting operators
    • Zbl 1096.47018 MR 2176465
    • HALLER-DINTELMANN, R., & HIEBER, M. H∞-calculus for products of non-commuting operators. Math. Z. 251 (2005), 85-100. Zbl 1096.47018 MR 2176465
    • (2005) Math. Z. , Issue.251 , pp. 85-100
    • Haller-Dintelmann, R.1    Hieber, M.2
  • 26
    • 0242301439 scopus 로고    scopus 로고
    • Functional calculi for linear operators in vector-valued Lp-spaces via the transference principle
    • Zbl 0956.47008 MR 1659281
    • HIEBER, M., & PRÜSS, J. Functional calculi for linear operators in vector-valued Lp-spaces via the transference principle. Adv. Differential Equations 3 (1998), 847-872. Zbl 0956.47008 MR 1659281
    • (1998) Adv. Differential Equations , vol.3 , pp. 847-872
    • Hieber, M.1    Prüss, J.2
  • 27
    • 0035643602 scopus 로고    scopus 로고
    • The H1-calculus and sums of closed operators
    • Zbl 0992.47005 MR 1866491
    • KALTON, N., & WEIS, L. The H1-calculus and sums of closed operators, Math. Ann. 321 (2001), 319-345. Zbl 0992.47005 MR 1866491
    • (2001) Math. Ann. , vol.321 , pp. 319-345
    • Kalton, N.1    Weis, L.2
  • 28
    • 17044413547 scopus 로고    scopus 로고
    • Maximal Lp-regularity for parabolic equations, Fourier multiplier theorems and H∞-functional calculus
    • Springer, Berlin. Zbl 1097.47041 MR 2108959
    • KUNSTMANN, P. C., & WEIS, L. Maximal Lp-regularity for parabolic equations, Fourier multiplier theorems and H∞-functional calculus. In: Functional Analytic Methods for Evolution Equations, Lecture Notes in Math. 1855, Springer, Berlin (2004), 65-311. Zbl 1097.47041 MR 2108959
    • (2004) Functional Analytic Methods for Evolution Equations, Lecture Notes in Math. , vol.1855 , pp. 65-311
    • Kunstmann, P.C.1    Weis, L.2
  • 29
    • 85042569745 scopus 로고
    • On the regularity of solutions of the nonstationary Navier-Stokes equations
    • Springer, Berlin. Zbl 0435.35029 MR 0566007
    • MASUDA, K. On the regularity of solutions of the nonstationary Navier-Stokes equations. In: Approximation Methods for Navier-Stokes Problems, Lecture Notes in Math. 771, Springer, Berlin (1980), 360-370. Zbl 0435.35029 MR 0566007
    • (1980) Approximation Methods for Navier-Stokes Problems, Lecture Notes in Math. , vol.771 , pp. 360-370
    • Masuda, K.1
  • 30
    • 0009929355 scopus 로고
    • On the solvability of an evolution free boundary problem for the Navier-Stokes equations in Hölder spaces of functions
    • World Sci. River Edge, NJ. Zbl 0793.35072 MR 1190731
    • MOGILEVSKII, I. SH., & SOLONNIKOV, V.A. On the solvability of an evolution free boundary problem for the Navier-Stokes equations in Hölder spaces of functions. In: Mathematical Problems Relating to the Navier-Stokes Equation, Ser. Adv. Math. Appl. Sci. 11, World Sci., River Edge, NJ (1992), 105-181. Zbl 0793.35072 MR 1190731
    • (1992) Mathematical Problems Relating to the Navier-Stokes Equation, Ser. Adv. Math. Appl. Sci. , vol.11 , pp. 105-181
    • Mogilevskii, I.S.H.1    Solonnikov, V.A.2
  • 31
    • 11144291313 scopus 로고    scopus 로고
    • On the global existence of nonsteady motions of a fluid drop and their exponential decay to a uniform rigid rotation
    • Dept. Mat., Seconda Univ. Napoli, Caserta. Zbl pre02079309 MR 2051775
    • PADULA, M., & SOLONNIKOV, V. A. On the global existence of nonsteady motions of a fluid drop and their exponential decay to a uniform rigid rotation. In: Topics in Mathematical Fluid Mechanics, Quad. Mat. 10, Dept. Mat., Seconda Univ. Napoli, Caserta (2002), 185-218. Zbl pre02079309 MR 2051775
    • (2002) Topics in Mathematical Fluid Mechanics, Quad. Mat. , vol.10 , pp. 185-218
    • Padula, M.1    Solonnikov, V.A.2
  • 32
    • 34249936488 scopus 로고    scopus 로고
    • Existence of analytic solutions for the classical Stefan problem
    • Zbl 1130.35136 MR 2317935
    • PRÜSS, J., SAAL, J., & SIMONETT, G. Existence of analytic solutions for the classical Stefan problem. Math. Ann. 338 (2007), 703-755. Zbl 1130.35136 MR 2317935
    • (2007) Math. Ann. , vol.338 , pp. 703-755
    • Prüss, J.1    Saal, J.2    Simonett, G.3
  • 33
    • 58149248533 scopus 로고    scopus 로고
    • H1-calculus for the sum of noncommuting operators
    • Zbl 1132.47014 MR 2302505
    • PRÜSS, J., & SIMONETT, G. H1-calculus for the sum of noncommuting operators. Trans. Amer. Math. Soc. 359 (2007), 3549-3565. Zbl 1132.47014 MR 2302505
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 3549-3565
    • Prüss, J.1    Simonett, G.2
  • 34
    • 79955714063 scopus 로고    scopus 로고
    • Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
    • Banach Center Publications 86, Inst. Math., Polish Acad. Sci.. Zbl 1167.35555 MR 2571494
    • PRÜSS, J., & SIMONETT, G. Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension. In: Nonlocal and Abstract Parabolic Equations and Applications, Banach Center Publications 86, Inst. Math., Polish Acad. Sci. (2009), 265-285. Zbl 1167.35555 MR 2571494
    • (2009) Nonlocal and Abstract Parabolic Equations and Applications , pp. 265-285
    • Prüss, J.1    Simonett, G.2
  • 37
    • 51249177627 scopus 로고
    • On operators with bounded imaginary powers in Banach spaces
    • Zbl 0665.47015 MR 1038710
    • PRÜSS, J., & SOHR, H. On operators with bounded imaginary powers in Banach spaces. Math. Z. 203 (1990), 429-452. Zbl 0665.47015 MR 1038710
    • (1990) Math. Z. , vol.203 , pp. 429-452
    • Prüss, J.1    Sohr, H.2
  • 38
    • 0038685357 scopus 로고    scopus 로고
    • On a resolvent estimate of the interface problem for the Stokes system in a bounded domain
    • DOI 10.1016/S0022-0396(03)00023-8
    • SHIBATA, Y., & SHIMIZU, S. On a resolvent estimate of the interface problem for the Stokes system in a bounded domain. J. Differential Equations 191 (2003), 408-444. Zbl 1030.35134 MR 1978384 (Pubitemid 36802603)
    • (2003) Journal of Differential Equations , vol.191 , Issue.2 , pp. 408-444
    • Shibata, Y.1    Shimizu, S.2
  • 39
    • 67449151847 scopus 로고    scopus 로고
    • On a free boundary problem for the Navier-Stokes equations
    • MR 2293985
    • SHIBATA, Y., & SHIMIZU, S. On a free boundary problem for the Navier-Stokes equations. Differential Integral Equations 20 (2007), 241-276. MR 2293985
    • (2007) Differential Integral Equations , vol.20 , pp. 241-276
    • Shibata, Y.1    Shimizu, S.2
  • 40
    • 40749116936 scopus 로고    scopus 로고
    • q maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
    • Zbl 1145.35053 MR 2384339
    • q maximal regularity of the Neumann problem for the Stokes equations in a bounded domain. J. Reine Angew. Math. 615 (2008), 157-209. Zbl 1145.35053 MR 2384339
    • (2008) J. Reine Angew. Math. , vol.615 , pp. 157-209
    • Shibata, Y.1    Shimizu, S.2
  • 43
    • 0010055990 scopus 로고
    • Solvability of the problem of evolution of an isolated amount of a viscous incompressible capillary fluid
    • (in Russian); English transl.
    • SOLONNIKOV, V. A. Solvability of the problem of evolution of an isolated amount of a viscous incompressible capillary fluid. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 140 (1984), 179-186 (in Russian); English transl.
    • (1984) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.140 , pp. 179-186
    • Solonnikov, V.A.1
  • 44
    • 77958027154 scopus 로고
    • Zbl 0551.76022 MR 0765724
    • J. Soviet Math. 37 (1987). Zbl 0551.76022 MR 0765724
    • (1987) J. Soviet Math. , vol.37
  • 45
    • 0010058488 scopus 로고
    • Unsteady flow of a finite mass of a fluid bounded by a free surface
    • (in Russian); English transl.
    • SOLONNIKOV, V. A. Unsteady flow of a finite mass of a fluid bounded by a free surface. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 152 (1986), 137-157 (in Russian); English transl.
    • (1986) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.152 , pp. 137-157
    • Solonnikov, V.A.1
  • 46
    • 0002020779 scopus 로고
    • Zbl 0639.76035 MR 0869248
    • J. Soviet Math. 40 (1988), 672-686. Zbl 0639.76035 MR 0869248
    • (1988) J. Soviet Math. , vol.40 , pp. 672-686
  • 47
    • 0000499109 scopus 로고
    • Unsteady motions of a finite isolated mass of a self-gravitating fluid
    • in Russian; English transl.
    • SOLONNIKOV, V. A. Unsteady motions of a finite isolated mass of a self-gravitating fluid. Algebra i Analiz 1 (1989), no. 1, 207-249 (in Russian); English transl.
    • (1989) Algebra i Analiz , vol.1 , Issue.1 , pp. 207-249
    • Solonnikov, V.A.1
  • 48
    • 0039488666 scopus 로고
    • Zbl 0713.76044 MR 1015340
    • Leningrad Math. J. 1 (1990), no. 1, 227-276. Zbl 0713.76044 MR 1015340
    • (1990) Leningrad Math. J. , vol.1 , Issue.1 , pp. 227-276
  • 49
    • 4243240091 scopus 로고
    • Solvability of a problem on the evolution of a viscous incompressible fluid, bounded by a free surface, on a finite time interval
    • (in Russian); English transl.
    • SOLONNIKOV, V.A. Solvability of a problem on the evolution of a viscous incompressible fluid, bounded by a free surface, on a finite time interval. Algebra i Analiz 3 (1991), no. 1, 222-257 (in Russian); English transl.
    • (1991) Algebra i Analiz , vol.3 , Issue.1 , pp. 222-257
    • Solonnikov, V.A.1
  • 50
    • 3042870460 scopus 로고
    • Zbl 0850.76132 MR 1120848
    • St. Petersburg Math. J. 3 (1992), no. 1, 189-220. Zbl 0850.76132 MR 1120848
    • (1992) St. Petersburg Math. J. , vol.3 , Issue.1 , pp. 189-220
  • 51
    • 0001831250 scopus 로고    scopus 로고
    • On quasistationary approximation in the problem of motion of a capillary drop
    • J. Escher and G. Simonett (eds.) , Birkhäuser, Basel, Zbl 0919.35103 MR 1725589
    • SOLONNIKOV, V. A. On quasistationary approximation in the problem of motion of a capillary drop. In: Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume, J. Escher and G. Simonett (eds.), Birkhäuser, Basel (1999), 643-671. Zbl 0919.35103 MR 1725589
    • (1999) Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume , pp. 643-671
    • Solonnikov, V.A.1
  • 52
    • 77958023052 scopus 로고    scopus 로고
    • q -estimates for a solution to the problem about the evolution of an isolated amount of a fluid
    • Zbl 1054.35070 MR 2027457
    • q -estimates for a solution to the problem about the evolution of an isolated amount of a fluid. J. Math. Sci. (N.Y.) 117 (2003), 4237-4259. Zbl 1054.35070 MR 2027457
    • (2003) J. Math. Sci. (N.Y.) , vol.117 , pp. 4237-4259
    • Solonnikov, V.A.1
  • 54
    • 38349054050 scopus 로고
    • Two-phase free boundary problem for viscous incompressible thermo-capillary convection
    • Zbl 0845.35138 MR 1338355
    • TANAKA, N. Two-phase free boundary problem for viscous incompressible thermo-capillary convection. Japan J. Mech. 21 (1995), 1-42. Zbl 0845.35138 MR 1338355
    • (1995) Japan J. Mech. , vol.21 , pp. 1-42
    • Tanaka, N.1
  • 55
    • 0030556037 scopus 로고    scopus 로고
    • Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface
    • TANI, A. Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface. Arch. Ration. Mech. Anal. 133 (1996), 299-331. Zbl 0857.76026 MR 1389902 (Pubitemid 126343946)
    • (1996) Archive for Rational Mechanics and Analysis , vol.133 , Issue.4 , pp. 299-331
    • Tani, A.1
  • 56
    • 21844524710 scopus 로고
    • Large-time existence of surface waves in incompressible viscous fluids with or without surface tension
    • Zbl 0844.76025 MR 1346360
    • TANI, A., & TANAKA, N. Large-time existence of surface waves in incompressible viscous fluids with or without surface tension. Arch. Ration. Mech. Anal. 130 (1995), 303-304. Zbl 0844.76025 MR 1346360
    • (1995) Arch. Ration. Mech. Anal. , vol.130 , pp. 303-304
    • Tani, A.1    Tanaka, N.2
  • 57
    • 0038895892 scopus 로고
    • On the Navier-Stokes flow down an inclined plane
    • TERAMATO, Y. On the Navier-Stokes flow down an inclined plane. J. Math. Kyoto Univ. 32 (1992), 593-619.
    • (1992) J. Math. Kyoto Univ. , vol.32 , pp. 593-619
    • Teramato, Y.1
  • 58
    • 0003295738 scopus 로고
    • Theory of function spaces
    • Birkhäuser, Basel. Zbl 0546.46027 MR 0781540
    • TRIEBEL, H. Theory of Function Spaces. Monogr. Math. 78, Birkhäuser, Basel (1983). Zbl 0546.46027 MR 0781540
    • (1983) Monogr. Math. , vol.78
    • Triebel, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.