-
Previous Article
A characterization of the symmetric steady water waves in terms of the underlying flow
- DCDS Home
- This Issue
-
Next Article
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.
doi: 10.1017/jfm.2012.490. |
[2] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
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, 81 (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.
doi: 10.3934/cpaa.2012.11.1397. |
[5] |
A. Constantin, Mean velocities in a Stokes wave,, Arch. Ration. Mech. Anal., 207 (2013), 907.
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.
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.
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.
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.
doi: 10.1002/cpa.3046. |
[10] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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, (1997).
doi: 10.1017/CBO9780511624056. |
[22] |
I. G. Jonsson, Wave-current interactions. In: The Sea ,, Wiley, (1990). Google Scholar |
[23] |
J. Lighthill, Waves in Fluids,, Cambridge Mathematical Library, (2001).
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.
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.
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,, , (). Google Scholar |
[27] |
A.-V. Matioc and B.-V. Matioc, On the symmetry of periodic gravity water waves with vorticity,, Differential Integral Equations, 26 (2013), 129.
|
[28] |
B.-V. Matioc, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity,, Int. Math. Res. Not., 17 (2011), 3858.
doi: 10.1093/imrn/rnq235. |
[29] |
G. Thomas and G. Klopman, Wave-Current Interactions in the Nearshore Region,, WIT, (1997). Google Scholar |
[30] |
J. F. Toland, Stokes waves,, Topol. Methods Nonlinear Anal., 7 (1996), 1.
|
[31] |
E. Wahlén, Steady periodic capillary-gravity waves with vorticity,, SIAM J. Math. Anal., 38 (2006), 921.
doi: 10.1137/050630465. |
[32] |
E. Wahlén, Steady water waves with a critical layer,, J. Differential Equations, 246 (2009), 2468.
doi: 10.1016/j.jde.2008.10.005. |
[33] |
S. Walsh, Stratified steady periodic water waves,, SIAM J. Math. Anal., 41 (2009), 1054.
doi: 10.1137/080721583. |
[34] |
L.-J. Wang, Regularity of traveling periodic stratified water waves with vorticity,, Nonlinear Anal., 81 (2013), 247.
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.
doi: 10.1017/jfm.2012.490. |
[2] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
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, 81 (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.
doi: 10.3934/cpaa.2012.11.1397. |
[5] |
A. Constantin, Mean velocities in a Stokes wave,, Arch. Ration. Mech. Anal., 207 (2013), 907.
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.
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.
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.
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.
doi: 10.1002/cpa.3046. |
[10] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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, (1997).
doi: 10.1017/CBO9780511624056. |
[22] |
I. G. Jonsson, Wave-current interactions. In: The Sea ,, Wiley, (1990). Google Scholar |
[23] |
J. Lighthill, Waves in Fluids,, Cambridge Mathematical Library, (2001).
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.
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.
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,, , (). Google Scholar |
[27] |
A.-V. Matioc and B.-V. Matioc, On the symmetry of periodic gravity water waves with vorticity,, Differential Integral Equations, 26 (2013), 129.
|
[28] |
B.-V. Matioc, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity,, Int. Math. Res. Not., 17 (2011), 3858.
doi: 10.1093/imrn/rnq235. |
[29] |
G. Thomas and G. Klopman, Wave-Current Interactions in the Nearshore Region,, WIT, (1997). Google Scholar |
[30] |
J. F. Toland, Stokes waves,, Topol. Methods Nonlinear Anal., 7 (1996), 1.
|
[31] |
E. Wahlén, Steady periodic capillary-gravity waves with vorticity,, SIAM J. Math. Anal., 38 (2006), 921.
doi: 10.1137/050630465. |
[32] |
E. Wahlén, Steady water waves with a critical layer,, J. Differential Equations, 246 (2009), 2468.
doi: 10.1016/j.jde.2008.10.005. |
[33] |
S. Walsh, Stratified steady periodic water waves,, SIAM J. Math. Anal., 41 (2009), 1054.
doi: 10.1137/080721583. |
[34] |
L.-J. Wang, Regularity of traveling periodic stratified water waves with vorticity,, Nonlinear Anal., 81 (2013), 247.
doi: 10.1016/j.na.2012.11.009. |
[1] |
Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond. A new model for the emergence of blood capillary networks. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2021001 |
[2] |
Lisa Hernandez Lucas. Properties of sets of Subspaces with Constant Intersection Dimension. Advances in Mathematics of Communications, 2021, 15 (1) : 191-206. doi: 10.3934/amc.2020052 |
[3] |
Jianli Xiang, Guozheng Yan. The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021004 |
[4] |
Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020361 |
[5] |
Bilal Al Taki, Khawla Msheik, Jacques Sainte-Marie. On the rigid-lid approximation of shallow water Bingham. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 875-905. doi: 10.3934/dcdsb.2020146 |
[6] |
Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115 |
[7] |
Shanding Xu, Longjiang Qu, Xiwang Cao. Three classes of partitioned difference families and their optimal constant composition codes. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020120 |
[8] |
Kevin Li. Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021003 |
[9] |
Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020359 |
[10] |
Marta Biancardi, Lucia Maddalena, Giovanni Villani. Water taxes and fines imposed on legal and illegal firms exploiting groudwater. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021008 |
[11] |
Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control & Related Fields, 2021, 11 (1) : 169-188. doi: 10.3934/mcrf.2020032 |
[12] |
Wei-Chieh Chen, Bogdan Kazmierczak. Traveling waves in quadratic autocatalytic systems with complexing agent. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020364 |
[13] |
M. S. Lee, H. G. Harno, B. S. Goh, K. H. Lim. On the bang-bang control approach via a component-wise line search strategy for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 45-61. doi: 10.3934/naco.2020014 |
[14] |
Zaizheng Li, Qidi Zhang. Sub-solutions and a point-wise Hopf's lemma for fractional $ p $-Laplacian. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020293 |
[15] |
Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020456 |
[16] |
Abdollah Borhanifar, Maria Alessandra Ragusa, Sohrab Valizadeh. High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020355 |
[17] |
Zi Xu, Siwen Wang, Jinjin Huang. An efficient low complexity algorithm for box-constrained weighted maximin dispersion problem. Journal of Industrial & Management Optimization, 2021, 17 (2) : 971-979. doi: 10.3934/jimo.2020007 |
[18] |
Zhenzhen Wang, Tianshou Zhou. Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020323 |
[19] |
Wei Feng, Michael Freeze, Xin Lu. On competition models under allee effect: Asymptotic behavior and traveling waves. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5609-5626. doi: 10.3934/cpaa.2020256 |
[20] |
Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020075 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]