Index
Alinhac’s good unknown, 71
Almost full justification, 169, 240, 298
Asymptotic regime, 23, 103
Camassa-Holm, 197, 212
deep water, 218, 222, 265
Kadomtsev-Petviashvili, 104, 188, 263
Kawahara, 262
Korteweg-de Vries, 104, 178, 261
long wave, 104, 204
long wave large topography, 129, 133
long wave small topography, 129, 145,
168
shallow water, 103, 123, 158, 165, 167,
205, 259
shallow water medium amplitude small
topography, 128
shallow water medium nonflat
topography, 128
shallow water with small topography, 127
weakly transverse Kawahara, 264
Atwood number, 9
Averaged velocity, 151
asymptotic expansion, 80
definition, 78
moving bottom, 79, 281
BBM equation, 181, 204
full justification, 204
weakly transverse, 190
Benjamin-Feir instability, 241
Benney-Roskes model
full dispersion, 231
standard, 232
Beppo-Levi spaces, 39
Biot-Savart’s law, 9
Bond number, 250
rescaled, 259
Boussinesq system, 130
full justification, 169
fully symmetric, 142, 143, 164, 169, 260
local existence and stability, 164
with four-parameter improved dispersion,
137, 170
with moving bottom, 145
with surface tension, 260
Boussinesq-Peregrine, 129
energy conservation, 172
with four-parameter improved dispersion,
139
with one-parameter improved dispersion,
132
with surface tension, 260
with three-parameter improved
dispersion, 134, 135
Camasa-Holm equation, 202
Camassa-Holm/Degasperis-Procesi type
equations
for the surface elevation, 199, 200
for the velocity, 197
full justification, 198, 199
wave breaking, 212
well-posedness, 208
with full dispersion, 214
with nonflat bottoms, 211
Commutator estimates
for paraproducts, 288
in Zygmund spaces, 291
on Rd, 286, 287
on a strip, 291
Conormal derivative, 19, 47, 62
Conserved quantity, 5, 172, 175
Consistency, 123, 135
Coriolis force, 33
Davey-Stewarston, 234
with full dispersion, 243
Deep water model, 217, 218, 300
almost full justification, 222
consistency, 220
infinite depth, 223
nonflat bottom, 219
with surface tension, 265
Degasperis-Procesi equation, 203
Diffeomorphism
admissible, 43, 62
regularizing, 45
Diffractive effects, 23
Dimensionless parameters, 13
Dirichlet-Dirichlet operator, 89, 278
Dirichlet-Neumann operator
and averaged velocity, 78
bilinear estimate, 66, 69, 76
319
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