Hydrodynamics with quadratic pressure. 1. General results
A. P. Chupakhin
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Abstract
A wide class of solutions of Euler
equations with quadratic pressure are
described. In Lagrangian coordinates,
these solutions linearize exactly
momentum equations and are characterized
by special initial data: the Jacobian
matrix of the initial velocity field has
constant algebraic invariants. The
equations are integrated using the
method of separation of the time and
Lagrangian coordinates. Time evolution
is defined by elliptic functions. The
solutions have a pole<!dash!>type
singularity at a finite time. A
representation for the velocity vortex
is given.
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