Communications in Mathematical Sciences

Volume 11 (2013)

Number 4

Analytical solutions for the free surface hydrostatic Euler equations

Pages: 993 – 1010



A. C. Boulanger (Laboratoire Jacques-Louis Lions, Univ Paris 06, Paris, France)

M. O. Bristeau (CETMEF, Margny les Compiègne, France)

J. Sainte-Marie (CETMEF, Margny les Compiègne, France)


In this paper we propose a large set of analytical solutions (FRESH-ASSESS) for the hydrostatic incompressible Euler system in 2d and 3d. These solutions mainly concern free surface flows but partially free surface flows are also considered. These analytical solutions can be especially useful for the validation of numerical schemes.


incompressible Euler equations, analytical solutions, free surface flows, entropic shocks

2010 Mathematics Subject Classification

35Q30, 35Q35, 76D05

Published 15 June 2013