On one system of the Burgers equations arising in the two-velocity hydrodynamics

Algebra, Analysis and Quantum Probability

Imomnazarov, Kholmatzhon^1 ; Mamasoliyev, Baxtier^2 ; Vasiliev, Georgy^1

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the RAS, Novosibirsk, Russia^1

National University of Uzbekistan, Mechanics and Mathematics Faculty, Tashkent, Uzbekistan^2

关键词: Burgers equations;    Cauchy problems;    Existence and uniqueness of solution;    Kinetic friction coefficient;    One-dimensional Burgers equation;    One-dimensional systems;    Weak approximation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012024/pdf
DOI  :  10.1088/1742-6596/697/1/012024

来源: IOP

【 摘 要 】

A system of the Burgers equations of the two-velocity hydrodynamics is constructed. We consider the Cauchy problem in the case of a one-dimensional system. We have obtained a formula for solving the Cauchy problem and the estimate of the stability of this solution. It is shown that with disappearance of the kinetic friction coefficient, which is responsible for the energy dissipation, this formula turns to the famous Cauchy problem for the one-dimensional Burgers equation. The existence and uniqueness of solutions to the Cauchy problem for the one-dimensional systems of the Burgers type are proved using the method of weak approximation.