Geodesic
On a system of equations describing surface waves
Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 119-156

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A new system of equations is proposed which describes surface waves in a fluid. The basic conservation laws are found for this system. The Cauchy problem for this system is considered, and the existence of a global solution (in time), the breakdown of a solution in finite time, and the smoothing of a discontinuous initial perturbation are studied. 
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     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {On a system of equations describing surface waves},
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P. I. Naumkin; I. A. Shishmarev. On a system of equations describing surface waves. Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 119-156. http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a5/