On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics.

*(English. Russian original)*Zbl 0829.35095
Math. Notes 55, No. 3, 243-250 (1994); translation from Mat. Zametki 55, No. 3, 11-20 (1994).

For a system of two-dimensional nonlinear equations of hydrodynamics taking into account the earth’s rotation, we deduce the chain of equations which contain a number of unfixed parameters that makes it possible to obtain the link of functions which define the principal term of the asymptotic representation of the solution. The closing of the obtained chain of ordinary equations is carried out. As was assumed, the center position of the weak singularity calculated by using the asymptotic representation for a solution of the initial nonlinear system can model the typhoon motion trajectory in the atmosphere of the rotating earth.

We perform numerical analysis of corresponding differential equations for investigating the trajectory motion of the weak point-type singularity. By comparing the numerical data with the trajectory motion of the real typhoon, we observe their quite good qualitative coincidence. Further, the numerical analysis shows that the trajectory motion of the singularity center depends weakly on the initial conditions, that is, in fact, the position of the singularity center can be determined by a system of equations which contains far less equations.

We perform numerical analysis of corresponding differential equations for investigating the trajectory motion of the weak point-type singularity. By comparing the numerical data with the trajectory motion of the real typhoon, we observe their quite good qualitative coincidence. Further, the numerical analysis shows that the trajectory motion of the singularity center depends weakly on the initial conditions, that is, in fact, the position of the singularity center can be determined by a system of equations which contains far less equations.

##### MSC:

35Q35 | PDEs in connection with fluid mechanics |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

86A10 | Meteorology and atmospheric physics |

##### Keywords:

chain of equations; closing; position of the weak singularity; typhoon motion trajectory in the atmosphere; numerical analysis
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\textit{V. V. Bulatov} et al., Math. Notes 55, No. 3, 1 (1994; Zbl 0829.35095); translation from Mat. Zametki 55, No. 3, 11--20 (1994)

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