메뉴 건너뛰기




Volumn 53, Issue 2, 2000, Pages 175-206

New similarity solutions of the unsteady incompressible boundary-layer equations

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYER FLOW; EQUATIONS OF MOTION; INCOMPRESSIBLE FLOW; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; UNSTEADY FLOW; VISCOUS FLOW;

EID: 0033738672     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/53.2.175     Document Type: Article
Times cited : (62)

References (67)
  • 1
    • 18944400520 scopus 로고
    • New similarity reductions of the Boussinesq equation
    • P. A. Clarkson and M. D. Kruskal, New similarity reductions of the Boussinesq equation. J. Math. Phys. 30 (1989) 2201-2213.
    • (1989) J. Math. Phys. , vol.30 , pp. 2201-2213
    • Clarkson, P.A.1    Kruskal, M.D.2
  • 3
    • 84935573705 scopus 로고
    • Further solutions of the Falkner-Skan equation
    • K. Stewartson, Further solutions of the Falkner-Skan equation. Proc. Camb. phil. Soc. 50 (1954) 454-465.
    • (1954) Proc. Camb. Phil. Soc. , vol.50 , pp. 454-465
    • Stewartson, K.1
  • 4
    • 0003026378 scopus 로고
    • Grenzschichten in flüssigkeiten mit kleiner reibung
    • H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. U. Phys. 56 (1908) 1-37.
    • (1908) Z. Math. U. Phys. , vol.56 , pp. 1-37
    • Blasius, H.1
  • 5
    • 0000960029 scopus 로고
    • Die grenzschicht an einem in den gleichförmigen flüssigkeitsstrom eingetauchten geraden kreiszylinder
    • K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers J. 326 (1911) 321-410.
    • (1911) Dinglers J. , vol.326 , pp. 321-410
    • Hiemenz, K.1
  • 6
    • 0001520256 scopus 로고
    • Solutions of the boundary-layer equations
    • V. M. Falkner and S. W. Skan, Solutions of the boundary-layer equations. Phil. Mag. (7) 12 (1931) 865-896.
    • (1931) Phil. Mag. , vol.12 , Issue.7 , pp. 865-896
    • Falkner, V.M.1    Skan, S.W.2
  • 7
    • 33748716786 scopus 로고
    • Laminare strahlausbreitung
    • H. Schlichting, Laminare Strahlausbreitung. Z. angew. Math. Mech. 13 (1933) 260-263.
    • (1933) Z. Angew. Math. Mech. , vol.13 , pp. 260-263
    • Schlichting, H.1
  • 8
    • 0000620783 scopus 로고
    • The plane jet
    • G. Bickley, The plane jet. Phil. Mag. 23 (1937) 727-731.
    • (1937) Phil. Mag. , vol.23 , pp. 727-731
    • Bickley, G.1
  • 9
    • 0013210876 scopus 로고
    • The laminar boundary layer on oscillating plates and cylinders
    • M. B. Glauert, The laminar boundary layer on oscillating plates and cylinders. J. Fluid Mech. 1 (1956) 97-110.
    • (1956) J. Fluid Mech. , vol.1 , pp. 97-110
    • Glauert, M.B.1
  • 10
    • 0038418507 scopus 로고
    • On the motion of solid bodies through viscous liquids
    • Lord Rayleigh, On the motion of solid bodies through viscous liquids. Phil. Mag. (6) 21 (1911) 697-711.
    • (1911) Phil. Mag. , vol.21 , Issue.6 , pp. 697-711
    • Rayleigh, L.1
  • 11
  • 12
    • 44949283480 scopus 로고
    • Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation
    • P. A. Clarkson and P. Winternitz, Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Physica D49 (1991) 257-272.
    • (1991) Physica , vol.D49 , pp. 257-272
    • Clarkson, P.A.1    Winternitz, P.2
  • 14
    • 0016116325 scopus 로고
    • Semisimilar solutions to unsteady boundary-layer flows including separation
    • J. C. Williams and W. D. Johnson, Semisimilar solutions to unsteady boundary-layer flows including separation. AIAA J. 12 (1974) 1388-1393.
    • (1974) AIAA J. , vol.12 , pp. 1388-1393
    • Williams, J.C.1    Johnson, W.D.2
  • 15
    • 0025481603 scopus 로고
    • A class of solutions of the boundary-layer equations
    • G. I. Burdé, A class of solutions of the boundary-layer equations. Fluid Dynamics 25 (1990) 201-207.
    • (1990) Fluid Dynamics , vol.25 , pp. 201-207
    • Burdé, G.I.1
  • 16
    • 0028428663 scopus 로고
    • The construction of special explicit solutions of the boundary-layer equations - Steady flows
    • _, The construction of special explicit solutions of the boundary-layer equations - steady flows. Q. Jl Mech. appl. Math 47 (1994) 247-260.
    • (1994) Q. Jl Mech. Appl. Math , vol.47 , pp. 247-260
  • 17
    • 0029403953 scopus 로고
    • The construction of special explicit solutions of the boundary-layer equations - Unsteady flows
    • _, The construction of special explicit solutions of the boundary-layer equations - unsteady flows. Ibid. 48 (1995) 611-633.
    • (1995) Q. Jl Mech. Appl. Math , vol.48 , pp. 611-633
  • 18
    • 0010237431 scopus 로고    scopus 로고
    • New similarity reductions of the steady-state boundary-layer equations
    • _, New similarity reductions of the steady-state boundary-layer equations. J. Phys. A: Math. Gen. 29 (1996) 1665-1683.
    • (1996) J. Phys. A: Math. Gen. , vol.29 , pp. 1665-1683
  • 19
    • 0030216397 scopus 로고    scopus 로고
    • Similarity solutions for steady laminar convection along heated plates with variable oblique suction: Newtonian and Darcian fluid flow
    • P. D. Weidman and M.F. Amberg, Similarity solutions for steady laminar convection along heated plates with variable oblique suction: Newtonian and Darcian fluid flow. Q. Jl Mech. appl. Math. 49 (1996) 373-403.
    • (1996) Q. Jl Mech. Appl. Math. , vol.49 , pp. 373-403
    • Weidman, P.D.1    Amberg, M.F.2
  • 20
    • 0004065402 scopus 로고
    • Similiarity methods for differential equations
    • Springer, New York
    • G. W. Bluman and J. D. Cole, Similiarity Methods for Differential Equations, Applied Mathematical Sciences 13 (Springer, New York 1974).
    • (1974) Applied Mathematical Sciences , vol.13
    • Bluman, G.W.1    Cole, J.D.2
  • 21
    • 0003339099 scopus 로고
    • Symmetries and differential equations
    • Springer, New York
    • G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Applied Mathematical Sciences 81 (Springer, New York 1989).
    • (1989) Applied Mathematical Sciences , vol.81
    • Bluman, G.W.1    Kumei, S.2
  • 25
    • 0003317855 scopus 로고
    • Applications of lie groups to differential equations
    • 2nd edition Springer, New York
    • P. J. Olver, Applications of Lie groups to Differential Equations, Graduate Texts in Mathematics 107, 2nd edition (Springer, New York 1993).
    • (1993) Graduate Texts in Mathematics , vol.107
    • Olver, P.J.1
  • 30
    • 0025463468 scopus 로고
    • Similarity solutions of the two-dimensional unsteady boundary-layer equations
    • P. K. H. Ma and W. H. Hui, Similarity solutions of the two-dimensional unsteady boundary-layer equations. J. Fluid Mech. 216 (1990) 537-559.
    • (1990) J. Fluid Mech. , vol.216 , pp. 537-559
    • Ma, P.K.H.1    Hui, W.H.2
  • 31
    • 84974510063 scopus 로고
    • A differential constraints approach to partial invariance
    • J. Ondich, A differential constraints approach to partial invariance. Europ. J. Appl. Math. 6 (1995) 631-637.
    • (1995) Europ. J. Appl. Math. , vol.6 , pp. 631-637
    • Ondich, J.1
  • 32
    • 0005103541 scopus 로고
    • Theory of consistency and methods of integrating systems of nonlinear partial differential equations
    • Leningrad (Russian)
    • N. N. Yanenko, Theory of consistency and methods of integrating systems of nonlinear partial differential equations. In Proceedings of the Fourth All-Union Mathematics Congress (Leningrad 1964) 247-259 (Russian).
    • (1964) Proceedings of the Fourth All-Union Mathematics Congress , pp. 247-259
    • Yanenko, N.N.1
  • 33
    • 46149142625 scopus 로고
    • The construction of special solutions to partial differential equations
    • P. J. Olver and P. Rosenau, The construction of special solutions to partial differential equations. Phys. Lett. A 114 (1986) 107-112.
    • (1986) Phys. Lett. A , vol.114 , pp. 107-112
    • Olver, P.J.1    Rosenau, P.2
  • 34
    • 0023327684 scopus 로고
    • Group-invariant solutions of differential equations
    • _ and _, Group-invariant solutions of differential equations. SIAM J. appl. Math. 47 (1987) 263-275.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 263-275
  • 35
    • 0000478462 scopus 로고
    • The general similarity of the heat equation
    • G. W. Bluman and J. D. Cole, The general similarity of the heat equation. J. Math. Mech. 18 (1969) 1025-1042.
    • (1969) J. Math. Mech. , vol.18 , pp. 1025-1042
    • Bluman, G.W.1    Cole, J.D.2
  • 36
    • 0001678923 scopus 로고
    • Nonclassical symmetry reduction: Example of the Boussinesq equation
    • D. Levi and P. Winternitz, Nonclassical symmetry reduction: example of the Boussinesq equation. J. Phys. A: Math. Gen. 22 (1989) 2915-2924.
    • (1989) J. Phys. A: Math. Gen. , vol.22 , pp. 2915-2924
    • Levi, D.1    Winternitz, P.2
  • 38
    • 0001719798 scopus 로고
    • Conditional symmetry of the equations of mathematical physics
    • W. I. Fushchych, Conditional symmetry of the equations of mathematical physics. Ukrain. Math. J. 43 (1991) 1456-1470.
    • (1991) Ukrain. Math. J. , vol.43 , pp. 1456-1470
    • Fushchych, W.I.1
  • 41
    • 0010250789 scopus 로고    scopus 로고
    • The nonclassical group analysis of the heat equation
    • E. L. Mansfield, The nonclassical group analysis of the heat equation. J. Math. Anal. Appl. 231 (1999) 526-542.
    • (1999) J. Math. Anal. Appl. , vol.231 , pp. 526-542
    • Mansfield, E.L.1
  • 42
    • 33646984319 scopus 로고
    • Nonclassical symmetry reductions of the Boussinesq equation
    • P. A. Clarkson, Nonclassical symmetry reductions of the Boussinesq equation. Chaos, Solitons & Fractals 5 (1995) 2261-2301.
    • (1995) Chaos, Solitons & Fractals , vol.5 , pp. 2261-2301
    • Clarkson, P.A.1
  • 43
    • 0005144466 scopus 로고    scopus 로고
    • The classical, direct and nonclassical methods for symmetry reductions of nonlinear partial differential equations
    • _, D. K. Ludlow and T. J. Priestley, The classical, direct and nonclassical methods for symmetry reductions of nonlinear partial differential equations. Meth. appl. Anal. 4 (1997) 173-195.
    • (1997) Meth. Appl. Anal. , vol.4 , pp. 173-195
    • Ludlow, D.K.1    Priestley, T.J.2
  • 44
    • 84972500466 scopus 로고
    • On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
    • V. A. Galaktionov, On new exact blow-up solutions for nonlinear heat conduction equations with source and applications. Diff. Int. Eqns 3 (1990) 863-874.
    • (1990) Diff. Int. Eqns , vol.3 , pp. 863-874
    • Galaktionov, V.A.1
  • 45
    • 21844483286 scopus 로고
    • New exact solutions of Burgers's equation - An extension to the direct method of Clarkson and Kruskal
    • S. Hood, New exact solutions of Burgers's equation - an extension to the direct method of Clarkson and Kruskal. J. Math. Phys. 36 (1995) 1971-1990.
    • (1995) J. Math. Phys. , vol.36 , pp. 1971-1990
    • Hood, S.1
  • 46
    • 0039629669 scopus 로고    scopus 로고
    • Developments in similarity methods related to the pioneering work of Julian Cole
    • ed. L. P. Cook, V. Roytburd and M. Turin; SIAM, Philadelphia
    • G. W. Bluman and V. Shtelen, Developments in similarity methods related to the pioneering work of Julian Cole. In Mathematics is for Solving Problems (ed. L. P. Cook, V. Roytburd and M. Turin; SIAM, Philadelphia 1996) 105-117.
    • (1996) Mathematics is for Solving Problems , pp. 105-117
    • Bluman, G.W.1    Shtelen, V.2
  • 48
    • 84972091492 scopus 로고
    • Nonclassical symmetry reductions and exact solutions of the Zabalotskaya-Khokhlov equation
    • P. A. Clarkson and S. Hood, Nonclassical symmetry reductions and exact solutions of the Zabalotskaya-Khokhlov equation. Europ. J. appl. Math. 3 (1992) 381-414.
    • (1992) Europ. J. Appl. Math. , vol.3 , pp. 381-414
    • Clarkson, P.A.1    Hood, S.2
  • 49
    • 21344480376 scopus 로고
    • New symmetry reductions and exact solutions of the Davey-Stewartson equation. I. Reductions to ordinary differential equations
    • _ and _, New symmetry reductions and exact solutions of the Davey-Stewartson equation. I. Reductions to ordinary differential equations. J. Math. Phys. 35 (1994) 255-283.
    • (1994) J. Math. Phys. , vol.35 , pp. 255-283
  • 50
    • 0040121940 scopus 로고    scopus 로고
    • Nonclassical symmetry reductions of the two-dimensional incompressible Navier-Stokes equations
    • D. K. Ludlow, P. A. Clarkson and A. P. Bassom, Nonclassical symmetry reductions of the two-dimensional incompressible Navier-Stokes equations. Stud. appl. Math. 103 (1999) 183-240.
    • (1999) Stud. Appl. Math. , vol.103 , pp. 183-240
    • Ludlow, D.K.1    Clarkson, P.A.2    Bassom, A.P.3
  • 51
    • 0028768164 scopus 로고
    • Direct reduction and differential constraints
    • P. J. Olver, Direct reduction and differential constraints. Proc. R. Soc. A 444 (1994) 509-523.
    • (1994) Proc. R. Soc. A , vol.444 , pp. 509-523
    • Olver, P.J.1
  • 52
    • 21344479980 scopus 로고
    • Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson-Kruskal
    • D. Arrigo, P. Broadbridge and J. M. Hill, Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson-Kruskal. J. Math. Phys 34 (1993) 4692-4703.
    • (1993) J. Math. Phys , vol.34 , pp. 4692-4703
    • Arrigo, D.1    Broadbridge, P.2    Hill, J.M.3
  • 54
    • 0001424046 scopus 로고
    • Similarity reductions of partial differential equations
    • E. Pucci, Similarity reductions of partial differential equations. J. Phys. A: Math. Gen. 25 (1992) 2631-2640.
    • (1992) J. Phys. A: Math. Gen. , vol.25 , pp. 2631-2640
    • Pucci, E.1
  • 57
    • 0001744933 scopus 로고
    • Unsteady viscous flow in the vicinity of a stagnation point
    • N. Rott, Unsteady viscous flow in the vicinity of a stagnation point. Q. appl. Math. 13 (1956) 444-451.
    • (1956) Q. Appl. Math. , vol.13 , pp. 444-451
    • Rott, N.1
  • 59
    • 0031522251 scopus 로고    scopus 로고
    • New solutions for laminar boundary layers with cross flow
    • P. D. Weidman, New solutions for laminar boundary layers with cross flow. Z. angew. Math. Phys. 48 (1997) 341-356.
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 341-356
    • Weidman, P.D.1
  • 60
    • 0030821104 scopus 로고    scopus 로고
    • Boundary layer similarity flow driven by power-law shear
    • P. D. Weidman, D. G. Kubitschek and S. N. Brown, Boundary layer similarity flow driven by power-law shear. Acta Mech. 120 (1997) 199-215.
    • (1997) Acta Mech. , vol.120 , pp. 199-215
    • Weidman, P.D.1    Kubitschek, D.G.2    Brown, S.N.3
  • 61
    • 0042173311 scopus 로고
    • Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes
    • J. Chazy, Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes. Acta Math. 34 (1911) 317-385.
    • (1911) Acta Math. , vol.34 , pp. 317-385
    • Chazy, J.1
  • 63
    • 0029703994 scopus 로고    scopus 로고
    • Symmetry and the Chazy equation
    • P. A. Clarkson and P. J. Olver, Symmetry and the Chazy equation. J. Diff. Eqns 124 (1996) 225-246.
    • (1996) J. Diff. Eqns , vol.124 , pp. 225-246
    • Clarkson, P.A.1    Olver, P.J.2
  • 64
    • 36749106124 scopus 로고
    • A connection between nonlinear evolution equations and ordinary differential equations of Painlevé type
    • M. J. Ablowitz, A. Ramani and H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of Painlevé type. J. Math. Phys. 21 (1980) 715-721.
    • (1980) J. Math. Phys. , vol.21 , pp. 715-721
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 65
    • 0031148294 scopus 로고    scopus 로고
    • On the effects of suction and injection on the absolute instability of the rotating-disk boundary layer
    • R. J. Lingwood, On the effects of suction and injection on the absolute instability of the rotating-disk boundary layer. Phys. Fluids 9 (1997) 1317-1328.
    • (1997) Phys. Fluids , vol.9 , pp. 1317-1328
    • Lingwood, R.J.1
  • 66
    • 0032261957 scopus 로고    scopus 로고
    • Active control of wave instabilities in three-dimensional compressible flows
    • M. S. Mughal, Active control of wave instabilities in three-dimensional compressible flows. Theoret. & Comput. Fluid Dyn. 12(1998) 195-217.
    • (1998) Theoret. & Comput. Fluid Dyn. , vol.12 , pp. 195-217
    • Mughal, M.S.1
  • 67
    • 0032475752 scopus 로고    scopus 로고
    • Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations
    • D. K. Ludlow, P. A. Clarkson and A. P. Bassom, Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. J. Phys. A: Math. Gen. 31 (1998) 7965-7980.
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 7965-7980
    • Ludlow, D.K.1    Clarkson, P.A.2    Bassom, A.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.