We prove global well-posedness for the lake equations. These equations arise to leading order in a low aspect ratio, low Froude number (i.e. low wave speed) and very small wave amplitude expansion of the three dimensional incompressible Euler equations in a basin with a free upper surface and a spatially varying bottom topography. Well-posedness means that there exists a solution, that it is unique and that it depends continuously on the data, i.e. the initial condition and the bottom topography.
Our approach follows the works of Yudovitch and Bardos in constructing the solutions as the inviscid limit of solutions to a system with artificial viscosity which is the analog of the Navier-Stokes with respect to the Euler equations. One of the main assumptions in the present work is a nondegenerate bottom topography.