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
Previous Page Next Page