Abstract:
A system of equations of isentropic gas motion with $n\ge2$ is classified in terms of zero-order conservation laws with the use of the method of $\mathbf{A}$-operators. New conservation laws are found to be valid only for potential isentropic motion of the Chaplygin gas. In this case, the greatest number of nontrivial conservation laws is obtained, with $n$ scalar conservation laws being nonlocal. Additional properties of symmetry of the considered equations associated with these conservation laws are indicated.
Keywords:conservation law, classification of equations of isentropic gas motion, nonlocal conservation laws, nonlocal symmetries, Chaplygin gas.
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