作者：Alvarez-Samaniego, Borys; Lannes, David
作者单位：Universite de Bordeaux; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a variable nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a wel...
作者：Guralnick, Robert M.; Tiep, Pham Huu
作者单位：State University System of Florida; University of Florida; University of Southern California
作者：Lau, Eike
作者单位：University of Bielefeld
摘要：Over p-adic Nagata rings, formal p-divisible groups are classified by nilpotent displays according to T. Zink. We extend this result to arbitrary p-adic rings. The proof uses the Grothendieck-Illusie deformation theory of truncated p-divisible groups.
