Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

We consider the so-called lake and great lake equations, which are shallow water equations
that describe the long-time motion of an inviscid, incompressible fluid contained in a shallow …

In this paper we consider a three‐dimensional planetary geostrophic viscous model of the
gyre‐scale mid‐latitude ocean. We show the global existence and uniqueness of the weak …

We present and discuss new shallow water equations that provide an estimate of the long-
time asymptotic effects of slowly varying bottom topography and weak hydrostatic imbalance …

We prove global well-posedness for the great lake equations. These equations arise to first
order in a low aspect ratio, low Froude number (ie low wave speed) and very small wave …

Abstract Holm (Proc R Soc A Math Phys Eng Sci 471 (2176): 20140963, 2015) introduced a
variational framework for stochastically parametrising unresolved scales of hydrodynamic …

The motion of an incompressible fluid confined to a shallow basin with a varying bottom
topography is considered. We introduce appropriate scalings into a three-dimensional …

We present and discuss new shallow-water equations that model the long-time effects of
slowly varying bottom topography and weak hydrostatic imbalance on the vertically …

We study so-called supercritical mean-field limits of systems of trapped particles moving
according to Newton's second law with either Coulomb/super-Coulomb or regular …

In this paper we study the mean-field limit of a system of point vortices for the lake equations.
These equations model the evolution of the horizontal component of the velocity field of a …