Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
email: rylov@ipmnet.ru
Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm
Updated
It is shown
that the Euler system of hydrodynamic equations for inviscid barotropic fluid
for density and velocity is not a complete system of dynamic equations for the
inviscicd barotropic fluid. It is only a closed subsystem of four dynamic
equation. The complete system of dynamic equation consists of seven dynamic
equations for seven dependent variables: density, velocity and labeling
(Lagrangian coordinates, considered as dependent variables). Solution of the
Cauchy problem for the Euler subsystem is unique. Solution of the Cauchy
problem for the complete hydrodynamic system, containing seven equations, is
unique only for irrotational flows. For vortical flows solution of the Cauchy
problem is not unique. The reason of the nonuniqueness is an interfusion, which
cannot be taken into account properly in the framework of hydrodynamics. There
are some arguments in favour of connection between interfusion and turbulence.
There is
text of the paper in English (pdf ) and
in Russian (pdf) and figures (ps)