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A characterization of the symmetric steady water waves in terms of the underlying flow
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Particle trajectories in extreme Stokes waves over infinite depth
Dispersion relations for periodic water waves with surface tension and discontinuous vorticity
1. | Institut für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria |
References:
[1] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-475.
doi: 10.1017/jfm.2012.490. |
[2] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[3] |
A. Constantin, Nonlinear water waves with applications to wave-current interactions and tsunamis, 81 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (2011).
doi: 10.1137/1.9781611971873. |
[4] |
A. Constantin, Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity, Commun. Pure Appl. Anal., 11 (2012), 1397-1406.
doi: 10.3934/cpaa.2012.11.1397. |
[5] |
A. Constantin, Mean velocities in a Stokes wave, Arch. Ration. Mech. Anal., 207 (2013), 907-917.
doi: 10.1007/s00205-012-0584-6. |
[6] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603.
doi: 10.1215/S0012-7094-07-14034-1. |
[7] |
A. Constantin and J. Escher, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech., 498 (2004), 171-181.
doi: 10.1017/S0022112003006773. |
[8] |
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 173 (2011), 559-568.
doi: 10.4007/annals.2011.173.1.12. |
[9] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481-527.
doi: 10.1002/cpa.3046. |
[10] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557.
doi: 10.1002/cpa.20299. |
[11] |
A. Constantin and W. Strauss, Periodic traveling gravity water waves with discontinuous vorticity, Arch. Ration. Mech. Anal., 202 (2011), 133-175.
doi: 10.1007/s00205-011-0412-4. |
[12] |
A. Constantin and W. A. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., 60 (2007), 911-950.
doi: 10.1002/cpa.20165. |
[13] |
A. Constantin and E. Varvaruca, Steady periodic water waves with constant vorticity: Regularity and local bifurcation, Arch. Ration. Mech. Anal., 199 (2011), 33-67.
doi: 10.1007/s00205-010-0314-x. |
[14] |
M. Ehrnström, J. Escher and E. Wahlén, Steady water waves with multiple critical layers, SIAM J. Math. Anal., 43 (2011), 1436-1456.
doi: 10.1137/100792330. |
[15] |
J. Escher, Regularity of rotational travelling water waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 370 (2012), 1602-1615.
doi: 10.1098/rsta.2011.0458. |
[16] |
J. Escher, A.-V. Matioc and B.-V. Matioc, On stratified steady periodic water waves with linear density distribution and stagnation points, J. Differential Equations, 251 (2011), 2932-2949.
doi: 10.1016/j.jde.2011.03.023. |
[17] |
D. Henry, Analyticity of the streamlines for periodic travelling free surface capillary-gravity water waves with vorticity, SIAM J. Math. Anal, 42 (2010), 3103-3111.
doi: 10.1137/100801408. |
[18] |
D. Henry, Analyticity of the free surface for periodic travelling capillary-gravity water waves with vorticity, J. Math. Fluid Mech., 14 (2012), 249-254.
doi: 10.1007/s00021-011-0056-z. |
[19] |
D. Henry, Dispersion relations for steady periodic water waves with an isolated layer of vorticity at the surface, Nonlinear Anal. Real World Appl., 14 (2013), 1034-1043.
doi: 10.1016/j.nonrwa.2012.08.015. |
[20] |
D. Henry and B.-V. Matioc, On the regularity of steady periodic stratified water waves, Commun. Pure Appl. Anal., 11 (2012), 1453-1464.
doi: 10.3934/cpaa.2012.11.1453. |
[21] |
R. S. Johnson, A modern Introduction to the Mathematical Theory of Water Waves, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1997.
doi: 10.1017/CBO9780511624056. |
[22] |
I. G. Jonsson, Wave-current interactions. In: The Sea , Wiley, New York, 1990. |
[23] |
J. Lighthill, Waves in Fluids, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2001, Reprint of the 1978 original.
doi: 10.1007/s002050100160. |
[24] |
C. I. Martin, Local bifurcation and regularity for steady periodic capillary-gravity water waves with constant vorticity, Nonlinear Anal. Real World Appl., 14 (2013), 131-149.
doi: 10.1016/j.nonrwa.2012.05.007. |
[25] |
C. I. Martin, Local bifurcation for steady periodic capillary water waves with constant vorticity, J. Math. Fluid Mech., 15 (2013), 155-170.
doi: 10.1007/s00021-012-0096-z. |
[26] |
C. I. Martin and B.-V. Matioc, Existence of capillary-gravity water waves with piecewise constant vorticity, arXiv:1302.5523. |
[27] |
A.-V. Matioc and B.-V. Matioc, On the symmetry of periodic gravity water waves with vorticity, Differential Integral Equations, 26 (2013), 129-140. |
[28] |
B.-V. Matioc, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity, Int. Math. Res. Not., 17 (2011), 3858-3871.
doi: 10.1093/imrn/rnq235. |
[29] |
G. Thomas and G. Klopman, Wave-Current Interactions in the Nearshore Region, WIT, Southampton, United Kingdom, 1997. |
[30] |
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal., 7 (1996), 1-48. |
[31] |
E. Wahlén, Steady periodic capillary-gravity waves with vorticity, SIAM J. Math. Anal., 38 (2006), 921-943 (electronic).
doi: 10.1137/050630465. |
[32] |
E. Wahlén, Steady water waves with a critical layer, J. Differential Equations, 246 (2009), 2468-2483.
doi: 10.1016/j.jde.2008.10.005. |
[33] |
S. Walsh, Stratified steady periodic water waves, SIAM J. Math. Anal., 41 (2009), 1054-1105.
doi: 10.1137/080721583. |
[34] |
L.-J. Wang, Regularity of traveling periodic stratified water waves with vorticity, Nonlinear Anal., 81 (2013), 247-263.
doi: 10.1016/j.na.2012.11.009. |
show all references
References:
[1] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-475.
doi: 10.1017/jfm.2012.490. |
[2] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[3] |
A. Constantin, Nonlinear water waves with applications to wave-current interactions and tsunamis, 81 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (2011).
doi: 10.1137/1.9781611971873. |
[4] |
A. Constantin, Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity, Commun. Pure Appl. Anal., 11 (2012), 1397-1406.
doi: 10.3934/cpaa.2012.11.1397. |
[5] |
A. Constantin, Mean velocities in a Stokes wave, Arch. Ration. Mech. Anal., 207 (2013), 907-917.
doi: 10.1007/s00205-012-0584-6. |
[6] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603.
doi: 10.1215/S0012-7094-07-14034-1. |
[7] |
A. Constantin and J. Escher, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech., 498 (2004), 171-181.
doi: 10.1017/S0022112003006773. |
[8] |
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 173 (2011), 559-568.
doi: 10.4007/annals.2011.173.1.12. |
[9] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481-527.
doi: 10.1002/cpa.3046. |
[10] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557.
doi: 10.1002/cpa.20299. |
[11] |
A. Constantin and W. Strauss, Periodic traveling gravity water waves with discontinuous vorticity, Arch. Ration. Mech. Anal., 202 (2011), 133-175.
doi: 10.1007/s00205-011-0412-4. |
[12] |
A. Constantin and W. A. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., 60 (2007), 911-950.
doi: 10.1002/cpa.20165. |
[13] |
A. Constantin and E. Varvaruca, Steady periodic water waves with constant vorticity: Regularity and local bifurcation, Arch. Ration. Mech. Anal., 199 (2011), 33-67.
doi: 10.1007/s00205-010-0314-x. |
[14] |
M. Ehrnström, J. Escher and E. Wahlén, Steady water waves with multiple critical layers, SIAM J. Math. Anal., 43 (2011), 1436-1456.
doi: 10.1137/100792330. |
[15] |
J. Escher, Regularity of rotational travelling water waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 370 (2012), 1602-1615.
doi: 10.1098/rsta.2011.0458. |
[16] |
J. Escher, A.-V. Matioc and B.-V. Matioc, On stratified steady periodic water waves with linear density distribution and stagnation points, J. Differential Equations, 251 (2011), 2932-2949.
doi: 10.1016/j.jde.2011.03.023. |
[17] |
D. Henry, Analyticity of the streamlines for periodic travelling free surface capillary-gravity water waves with vorticity, SIAM J. Math. Anal, 42 (2010), 3103-3111.
doi: 10.1137/100801408. |
[18] |
D. Henry, Analyticity of the free surface for periodic travelling capillary-gravity water waves with vorticity, J. Math. Fluid Mech., 14 (2012), 249-254.
doi: 10.1007/s00021-011-0056-z. |
[19] |
D. Henry, Dispersion relations for steady periodic water waves with an isolated layer of vorticity at the surface, Nonlinear Anal. Real World Appl., 14 (2013), 1034-1043.
doi: 10.1016/j.nonrwa.2012.08.015. |
[20] |
D. Henry and B.-V. Matioc, On the regularity of steady periodic stratified water waves, Commun. Pure Appl. Anal., 11 (2012), 1453-1464.
doi: 10.3934/cpaa.2012.11.1453. |
[21] |
R. S. Johnson, A modern Introduction to the Mathematical Theory of Water Waves, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1997.
doi: 10.1017/CBO9780511624056. |
[22] |
I. G. Jonsson, Wave-current interactions. In: The Sea , Wiley, New York, 1990. |
[23] |
J. Lighthill, Waves in Fluids, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2001, Reprint of the 1978 original.
doi: 10.1007/s002050100160. |
[24] |
C. I. Martin, Local bifurcation and regularity for steady periodic capillary-gravity water waves with constant vorticity, Nonlinear Anal. Real World Appl., 14 (2013), 131-149.
doi: 10.1016/j.nonrwa.2012.05.007. |
[25] |
C. I. Martin, Local bifurcation for steady periodic capillary water waves with constant vorticity, J. Math. Fluid Mech., 15 (2013), 155-170.
doi: 10.1007/s00021-012-0096-z. |
[26] |
C. I. Martin and B.-V. Matioc, Existence of capillary-gravity water waves with piecewise constant vorticity, arXiv:1302.5523. |
[27] |
A.-V. Matioc and B.-V. Matioc, On the symmetry of periodic gravity water waves with vorticity, Differential Integral Equations, 26 (2013), 129-140. |
[28] |
B.-V. Matioc, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity, Int. Math. Res. Not., 17 (2011), 3858-3871.
doi: 10.1093/imrn/rnq235. |
[29] |
G. Thomas and G. Klopman, Wave-Current Interactions in the Nearshore Region, WIT, Southampton, United Kingdom, 1997. |
[30] |
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal., 7 (1996), 1-48. |
[31] |
E. Wahlén, Steady periodic capillary-gravity waves with vorticity, SIAM J. Math. Anal., 38 (2006), 921-943 (electronic).
doi: 10.1137/050630465. |
[32] |
E. Wahlén, Steady water waves with a critical layer, J. Differential Equations, 246 (2009), 2468-2483.
doi: 10.1016/j.jde.2008.10.005. |
[33] |
S. Walsh, Stratified steady periodic water waves, SIAM J. Math. Anal., 41 (2009), 1054-1105.
doi: 10.1137/080721583. |
[34] |
L.-J. Wang, Regularity of traveling periodic stratified water waves with vorticity, Nonlinear Anal., 81 (2013), 247-263.
doi: 10.1016/j.na.2012.11.009. |
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