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On the symmetry of spatially periodic two-dimensional water waves
1. | Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, A-1090, Austria |
References:
[1] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom Pressure measurements, J. Fluid Mech., 726 (2013), 547-558.
doi: 10.1017/jfm.2013.253. |
[2] |
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. |
[3] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[4] |
A. Constantin, Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 2011.
doi: 10.1137/1.9781611971873. |
[5] |
A. Constantin, Estimating wave heights from pressure data at the bed, J. Fluid Mech., 743 (2014), 10pp.
doi: 10.1017/jfm.2014.81. |
[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] |
M. Ehrnström, H. Holden and X. Raynaud, Symmetric Waves Are Traveling Waves, International Mathematics Research Notices, 2009 (2009), 4578-4596.
doi: 10.1093/imrn/rnp100. |
[9] |
R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge Texts in Applied Mathematics, Cambridge, 1997.
doi: 10.1017/CBO9780511624056. |
[10] |
F. Kogelbauer, Recovery of the wave profile for irrotational periodic water waves from pressure measurements, Nonl. Anal.: Real World Appl., 22 (2015), 219-224.
doi: 10.1016/j.nonrwa.2014.09.003. |
[11] |
F. Kogelbauer, Symmetric irrotational water waves are traveling waves, J. Diff. Eq., 259 (2015), 5271-5275.
doi: 10.1016/j.jde.2015.06.025. |
[12] |
S. Lang, Complex Analysis, Graduate Texts in Mathematics, Springer, 2003. |
[13] |
B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow, Discrete Contin. Dyn. Syst., A 34 (2014), 3125-3133.
doi: 10.3934/dcds.2014.34.3125. |
[14] |
H. Okamoto and M. Shoji, The Mathematical Theory of Permanent Progressive Water-waves, World Scientific, 2001.
doi: 10.1142/4547. |
[15] |
G. Tulzer, On the symmetry of steady periodic water waves with stagnation points, Comm. Pure Appl. Anal., 11 (2012), 1577-1586.
doi: 10.3934/cpaa.2012.11.1577. |
show all references
References:
[1] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom Pressure measurements, J. Fluid Mech., 726 (2013), 547-558.
doi: 10.1017/jfm.2013.253. |
[2] |
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. |
[3] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[4] |
A. Constantin, Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 2011.
doi: 10.1137/1.9781611971873. |
[5] |
A. Constantin, Estimating wave heights from pressure data at the bed, J. Fluid Mech., 743 (2014), 10pp.
doi: 10.1017/jfm.2014.81. |
[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] |
M. Ehrnström, H. Holden and X. Raynaud, Symmetric Waves Are Traveling Waves, International Mathematics Research Notices, 2009 (2009), 4578-4596.
doi: 10.1093/imrn/rnp100. |
[9] |
R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge Texts in Applied Mathematics, Cambridge, 1997.
doi: 10.1017/CBO9780511624056. |
[10] |
F. Kogelbauer, Recovery of the wave profile for irrotational periodic water waves from pressure measurements, Nonl. Anal.: Real World Appl., 22 (2015), 219-224.
doi: 10.1016/j.nonrwa.2014.09.003. |
[11] |
F. Kogelbauer, Symmetric irrotational water waves are traveling waves, J. Diff. Eq., 259 (2015), 5271-5275.
doi: 10.1016/j.jde.2015.06.025. |
[12] |
S. Lang, Complex Analysis, Graduate Texts in Mathematics, Springer, 2003. |
[13] |
B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow, Discrete Contin. Dyn. Syst., A 34 (2014), 3125-3133.
doi: 10.3934/dcds.2014.34.3125. |
[14] |
H. Okamoto and M. Shoji, The Mathematical Theory of Permanent Progressive Water-waves, World Scientific, 2001.
doi: 10.1142/4547. |
[15] |
G. Tulzer, On the symmetry of steady periodic water waves with stagnation points, Comm. Pure Appl. Anal., 11 (2012), 1577-1586.
doi: 10.3934/cpaa.2012.11.1577. |
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