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 January 9, 2007
The Cuachy
problem for the 3D vortical flow of ideal barotropic fluid is considered. It is
shown that the solution of the Cauchy problem is unique, if one considers seven
dynamic equations for seven dependent variables: the density r, the velocity v and Lagrangian variables x ={ x_1,x _2,x_3}, labeling the fluid
particles. If one considers only the closed (Euler) system of four equations
for four dependent variables r ,v,
the solution is not unique. The fact is that the Euler system describes both
the fluid motion at fixing labeling and the evolution of the fluid labeling,
whose evolution is described by the Lin constraints (equations for variables x). If one ignores the Lin
constraints at the solution of the Euler system, (or one considers the Lin
constraints on the basis of the solution of the Euler system), nonunique
solution of the Cauchy problem is obtained.unification of the principles of
relativity with the nonrelativistic quantum principles..
There is
text of the paper in English (ps, pdf ) and in Russian (ps, pdf) and figures (ps)