Global Existence for Capillary Water Waves
Copyright policy )Global Existence for Capillary Water Waves
Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space‐time resonance method and commuting vector fields. © 2015 Wiley Periodicals, Inc.
- New York University United States
- Courant Institute of Mathematical Sciences United States
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Asymptotic behavior of solutions to PDEs, Existence problems for PDEs: global existence, local existence, non-existence, PDEs in connection with fluid mechanics, Capillarity (surface tension) for incompressible inviscid fluids, 35B40, 37L50, 76D03, 76D33, 76D45, capillary water waves equations, Mathematics - Analysis of PDEs, FOS: Mathematics, global existence and scattering, Analysis of PDEs (math.AP)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Asymptotic behavior of solutions to PDEs, Existence problems for PDEs: global existence, local existence, non-existence, PDEs in connection with fluid mechanics, Capillarity (surface tension) for incompressible inviscid fluids, 35B40, 37L50, 76D03, 76D33, 76D45, capillary water waves equations, Mathematics - Analysis of PDEs, FOS: Mathematics, global existence and scattering, Analysis of PDEs (math.AP)
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