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Weak Singularity for Two-Dimensional Nonlinear Equations of Hydrodynamics and Propagation of Shock Waves

Vitaly V. Bulatov·Yuriy V. Vladimirov·Vasily A. Vakorin
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Abstract

A system of two-dimensional nonlinear equations of hydrodynamics is considered. It is shown that for the this system in the general case a solution with weak discontinuity-type singularity behaves as a square root of S(x,y,t), where S(x,y,t)>0 is a smooth function. The necessary conditions and series of corresponding differential equations are obtained for the existence of a solution.

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Vitaly V. Bulatov, Yuriy V. Vladimirov, Vasily A. Vakorin. 2004-10-27. Weak Singularity for Two-Dimensional Nonlinear Equations of Hydrodynamics and Propagation of Shock Waves. https://arxiv.org/abs/math-ph/0410058

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