caa a22 4500 605515549 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0842-5 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0842-5 Gravity Capillary Standing Water Waves [Elektronische Daten] [Thomas Alazard, Pietro Baldi] The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the construction of small amplitude, standing (namely periodic in time and space, and not travelling) solutions of Sobolev regularity, for almost all values of the surface tension coefficient, and for a large set of time-frequencies. This is an existence result for a quasi-linear, Hamiltonian, reversible system of two autonomous pseudo-PDEs with small divisors. The proof is a combination of different techniques, such as a Nash-Moser scheme, microlocal analysis and bifurcation analysis. Springer-Verlag Berlin Heidelberg, 2015 Alazard Thomas Département de Mathématiques et Applications, Ecole Normale Supérieure, 45 rue d'Ulm, 75005, Paris, France aut Baldi Pietro Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126, Naples, Italy aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 741-830 0003-9527 217:3<741 2015 217 205 https://doi.org/10.1007/s00205-015-0842-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0842-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alazard Thomas Département de Mathématiques et Applications, Ecole Normale Supérieure, 45 rue d'Ulm, 75005, Paris, France aut NATIONALLICENCE 700 1- Baldi Pietro Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126, Naples, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 741-830 0003-9527 217:3<741 2015 217 205