Application of invariants of characteristics to construction of solutions without gradient catastrophe
Alexander V. Aksenov, Konstantin P. Druzhkov, Oleg V. Kaptsov
TL;DR
This paper classifies invariants of characteristics in isentropic gas dynamics and proposes a method to construct smooth solutions that avoid gradient catastrophe, supported by examples.
Contribution
It introduces a new approach to constructing smooth solutions without gradient catastrophe using invariants of characteristics in gas dynamics.
Findings
Classification of first-order invariants of characteristics.
Classification of second-order invariants for polytropic processes.
Examples of solutions without gradient catastrophe.
Abstract
The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants of characteristics are classified for polytropic processes. The infinite sequence of Darboux integrable systems is described. The approach to construction of smooth solutions without gradient catastrophe is proposed. Examples of solutions without gradient catastrophe are presented.
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