Almost global existence of solutions for space periodic capillaritygravity water waves equations
Almost global existence of solutions for space periodic capillaritygravity water waves equations

Massimiliano Berti, SISSA
Fine Hall 314
We prove that any solution of the Cauchy problem for the capillaritygravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size \ep , is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude \ep^{N} for any N, as soon as the initial data are smooth enough, and the gravitycapillarity parameters are taken outside an exceptional subset of zero measure.