Analyticity of the streamlines and of the free surface for periodic equatorial gravity water flows with vorticity

Toland, 1996, Stokes waves, Topol. Methods Nonlinear Anal., 7, 1, 10.12775/TMNA.1996.001 Clamond, 2013, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714, 463, 10.1017/jfm.2012.490 Constantin, 2006, The trajectories of particles in Stokes waves, Invent. Math., 166, 523, 10.1007/s00222-006-0002-5 Constantin, 2013, Mean velocities in a Stokes wave, Arch. Ration. Mech. Anal., 207, 907, 10.1007/s00205-012-0584-6 Constantin, 2010, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63, 533 Constantin, 2011, vol. 81 Jonsson, 1990, Wave–current interactions Thomas, 1997 Constantin, 2004, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57, 481, 10.1002/cpa.3046 Constantin, 2007, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140, 591, 10.1215/S0012-7094-07-14034-1 Constantin, 2004, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech., 498, 171, 10.1017/S0022112003006773 Matioc, 2013, On the symmetry of periodic gravity water waves with vorticity, Differential Integral Equations, 26, 129 Constantin, 2011, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 173, 559, 10.4007/annals.2011.173.1.12 Escher, 2012, Regularity of rotational travelling water waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 370, 1602, 10.1098/rsta.2011.0458 Henry, 2010, Analyticity of the streamlines for periodic travelling free surface capillary–gravity water waves with vorticity, SIAM J. Math. Anal., 42, 3103, 10.1137/100801408 Henry, 2012, Analyticity of the free surface for periodic travelling capillary–gravity water waves with vorticity, J. Math. Fluid Mech., 14, 249, 10.1007/s00021-011-0056-z Wang, 2013, Regularity of traveling periodic stratified water waves with vorticity, Nonlinear Anal., 81, 247, 10.1016/j.na.2012.11.009 Constantin, 2011, Steady periodic water waves with constant vorticity: regularity and local bifurcation, Arch. Ration. Mech. Anal., 199, 33, 10.1007/s00205-010-0314-x Ehrnström, 2011, Steady water waves with multiple critical layers, SIAM J. Math. Anal., 43, 1436, 10.1137/100792330 Martin, 2013, Local bifurcation and regularity for steady periodic capillary–gravity water waves with constant vorticity, Nonlinear Anal. RWA, 131, 10.1016/j.nonrwa.2012.05.007 Wahlén, 2009, Steady water waves with a critical layer, J. Differential Equations, 246, 2468, 10.1016/j.jde.2008.10.005 Martin, 2014, Existence of capillary–gravity water waves with piecewise constant vorticity, J. Differential Equations, 256, 3086, 10.1016/j.jde.2014.01.036 Constantin, 2011, Periodic traveling gravity water waves with discontinuous vorticity, Arch. Ration. Mech. Anal., 202, 133, 10.1007/s00205-011-0412-4 Matioc, 2011, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity, Int. Math. Res. Not., 17, 3858 Matioc, 2014, Capillary–gravity water waves with discontinuous vorticity: existence and regularity results, Comm. Math. Phys., 330, 859, 10.1007/s00220-014-1918-z Martin, 2014, Steady periodic water waves with unbounded vorticity: equivalent formulations and existence results, J. Nonlinear Sci., 10.1007/s00332-014-9201-1 Cushman-Roisin, 2011 Fedorov, 2009, Equatorial waves, 3679 Pedlosky, 1979 Constantin, 2012, An exact solution for equatorially trapped waves, J. Geophys. Res., 117 Constantin, 2012, On the modelling of equatorial waves, Geophys. Res. Lett., 39, L05602, 10.1029/2012GL051169 Constantin, 2013, On equatorial wind waves, Differential Integral Equations, 26, 237 Constantin, 2013, Some three-dimensional nonlinear equatorial flows, J. Phys. Oceanogr., 43, 165, 10.1175/JPO-D-12-062.1 Constantin, 2014, Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves, J. Phys. Oceanogr., 44, 781, 10.1175/JPO-D-13-0174.1 Henry, 2013, An exact solution for equatorial geophysical water waves with an underlying current, Eur. J. Mech. B Fluids, 38, 18, 10.1016/j.euromechflu.2012.10.001 Hsu, 2014, An exact solution for equatorial waves, Monatsh. Math., 10.1007/s00605-014-0618-2 Philander, 1980, The equatorial undercurrent revisited, Annu. Rev. Earth Planet Sci., 8, 191, 10.1146/annurev.ea.08.050180.001203 Gallagher, 2007, vol. 4 Henry, 2014, On the existence of equatorial wind waves, Nonlinear Anal., 101, 113, 10.1016/j.na.2014.01.018 Matioc, 2012, An exact solution for geophysical equatorial edge waves over a sloping beach, J. Phys. A, 45, 365501, 10.1088/1751-8113/45/36/365501 Henry, 2014, On the symmetry of steady equatorial wind waves, Nonlinear Anal. RWA, 18, 50, 10.1016/j.nonrwa.2014.01.009 Martin, 2014, Equatorial wind waves with capillary effects and stagnation points, Nonlinear Anal., 96, 1, 10.1016/j.na.2013.10.025 Buffoni, 2003 Gilbarg, 2001 Fraenkel, 2000, vol. 128 Kinderlehrer, 1978, Regularity in elliptic free boundary problems, J. Anal. Math., 34, 86, 10.1007/BF02790009 Escher, 1996, Analyticity of the interface in a free boundary problem, Math. Ann., 305, 439, 10.1007/BF01444233