\title{\bf{Numerical Modelling of bubble liquid in a teapot}
The Russian foundation for Basic Research supported this
investigation by grants No.99-99-99999} }
V.V. Vasya \index{V.V. Vasya}
\thanks{Institute of Computational Mathematics and Mathematical
Geophysics SB RAS}, \, P.P. Petro \index{P.P. Petrov}
\thanks{Novosibirsk State University } }

The numerical results of computer modelling of bubble liquid
motion in a teapot. The stability of the system at small


A mathematical model of bubble liquid motion in a teapot has been
created in paper \cite{1}. The model is based in three general
principles. Validity of the conservation laws for mass,momentum,
energy and entropy is postulated in the continual approximation.


\section{Basic equations of bubble liquid model}
The equations of conservation laws:

\frac{\partial \rho}{\partial t} + \nabla\cdot{\bf j} = 0,
\label{eq1} \\
 \frac{\partial j_i}{\partial t} + \partial_k\Pi_{ik} = 0,
 \label{eq2} \\
 \frac{\partial S}{\partial t} + \nabla\cdot(\frac{S}{\rho}{\bf j}) = 0.

In equations (\ref{eq1}) - (\ref{eq3}), $\rho$ is density of a
liquid, ${\bf j}$ is impulse, $S$ is  entropy.


\section{Numerical solution}
Complete results of the numerical modelling of bubble liquid in a
teapot in Fig. 1.

\caption{The density of bubble liquid in an teapot}


\bibitem{1} Rockafellar~R.T. Convex Analysis. -- Princeton:
University Press, 1970.

\bibitem{2} Tocher K.D.  The application of automatic computers to
sampling experiments~// J. Royal Statist. Soc. Ser. B. -- 1954. --
Vol.~16, N~1. -- P.~39--61.

\bibitem{3} Marsaglia G. Random numbers fall mainly in the planes~// Proc.
Nat. Acad. Sci. USA. -- 1968. -- Vol.~61. -- P.~23--25.