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Energy-minimising parallel flows with prescribed vorticity distribution
Non-existence of global energy minimisers in Stokes waves problems
1. | St John's College, Cambridge, CB2 1TP |
References:
[1] |
P. Baldi and J. F. Toland, Steady periodic water waves under nonlinear elastic membranes, J. Reine Angew. Math., 652 (2011), 67-112.
doi: 10.1515/CRELLE.2011.015. |
[2] |
B. Buffoni and G. R. Burton, On the stability of travelling waves with vorticity obtained by minimisation,, to appear in Nonlinear Differential Equations Appl., ().
doi: 10.1007/s00030-013-0223-4. |
[3] |
G. R. Burton and J. F. Toland, Surface waves on steady perfect-fluid flows with vorticity, Comm. Pure Appl. Math., LXIV (2011), 975-1007.
doi: 10.1002/cpa.20365. |
[4] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., LVII (2004), 481-527.
doi: 10.1002/cpa.3046. |
[5] |
A. Constantin and W. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., LX (2007), 911-950.
doi: 10.1002/cpa.20165. |
[6] |
M.-L. Dubreil-Jacotin, Sur la détermination rigoureuse des ondes permanentes périodiques d'ampleur finie, J. Math. Pures Appl., 13 (1934), 217-291. |
[7] |
V. Kozlov and N. Kuznetsov, Steady free-surface vortical flows parallel to the horizontal bottom, Quart. J. Mech. Appl. Math., 64 (2011), 371-399.
doi: 10.1093/qjmam/hbr010. |
[8] |
E. Shargorodsky and J. F. Toland, Bernoulli Free-Boundary Problems, Memoirs of Amer. Math. Soc., 914, ISSN 0065-9266, Providence, RI, 2008.
doi: 10.1090/memo/0914. |
[9] |
W. A. Strauss, Steady water waves, Bull. Am. Math. Soc. (N.S.), 47 (2010), 671-694.
doi: 10.1090/S0273-0979-2010-01302-1. |
[10] |
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal., 7 (1996), 1-8. |
[11] |
J. F. Toland, Steady periodic hydroelastic waves, Arch. Rational Mech. Anal., 189 (2008), 325-362.
doi: 10.1007/s00205-007-0104-2. |
[12] |
J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution,, to appear in Discrete Continuous Dynam. Systems - A., ().
|
show all references
References:
[1] |
P. Baldi and J. F. Toland, Steady periodic water waves under nonlinear elastic membranes, J. Reine Angew. Math., 652 (2011), 67-112.
doi: 10.1515/CRELLE.2011.015. |
[2] |
B. Buffoni and G. R. Burton, On the stability of travelling waves with vorticity obtained by minimisation,, to appear in Nonlinear Differential Equations Appl., ().
doi: 10.1007/s00030-013-0223-4. |
[3] |
G. R. Burton and J. F. Toland, Surface waves on steady perfect-fluid flows with vorticity, Comm. Pure Appl. Math., LXIV (2011), 975-1007.
doi: 10.1002/cpa.20365. |
[4] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., LVII (2004), 481-527.
doi: 10.1002/cpa.3046. |
[5] |
A. Constantin and W. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., LX (2007), 911-950.
doi: 10.1002/cpa.20165. |
[6] |
M.-L. Dubreil-Jacotin, Sur la détermination rigoureuse des ondes permanentes périodiques d'ampleur finie, J. Math. Pures Appl., 13 (1934), 217-291. |
[7] |
V. Kozlov and N. Kuznetsov, Steady free-surface vortical flows parallel to the horizontal bottom, Quart. J. Mech. Appl. Math., 64 (2011), 371-399.
doi: 10.1093/qjmam/hbr010. |
[8] |
E. Shargorodsky and J. F. Toland, Bernoulli Free-Boundary Problems, Memoirs of Amer. Math. Soc., 914, ISSN 0065-9266, Providence, RI, 2008.
doi: 10.1090/memo/0914. |
[9] |
W. A. Strauss, Steady water waves, Bull. Am. Math. Soc. (N.S.), 47 (2010), 671-694.
doi: 10.1090/S0273-0979-2010-01302-1. |
[10] |
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal., 7 (1996), 1-8. |
[11] |
J. F. Toland, Steady periodic hydroelastic waves, Arch. Rational Mech. Anal., 189 (2008), 325-362.
doi: 10.1007/s00205-007-0104-2. |
[12] |
J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution,, to appear in Discrete Continuous Dynam. Systems - A., ().
|
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