Alexander A. Rodionov, “A hydrostatic model for an ideal fluid: group properties of equations and their solutions”, J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 3,Pages <nobr>320

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A hydrostatic model for an ideal fluid: group properties of equations and their solutions

Alexander A. Rodionov^ab

^a Institute of Computational Modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, 660036, Russia
^b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: Group properties of hydrostatic model equations of a layer motion in an ideal fluid on a function defining the free surface and the thickness of the fluid layer under the free boundary are studied. Examples of several exact solutions in Cartesian and cylindrical coordinates are given, they determine the free surface and the pressure on it.

Keywords: ideal fluid, hydrostatic model, group analysis, exact solutions.

UDC: 517.95+532

Received: 07.01.2015
Received in revised form: 24.02.2015
Accepted: 27.05.2015

Language: English

DOI: 10.17516/1997-1397-2015-8-3-320-326